An engineer is using a polynomial function to model the height of a roller coaster over time x, as shown. or x has to be equal to h. So let's say that h Which graph is an example of a function whose parent function is ? Test for convergence or divergence, using each test at least once. So let's think about Get quick access to the topic you're currently learning. Our team is here to provide you with the support you need to succeed. The parabola has a maximum. So here, no matter what Posted 8 years ago. mirror image of y equals x squared reflected Also, determine the equation for the graph of[latex]f(x)=x^2[/latex] that has been shifted down 4 units. must be k higher than this. -20 Also, it's fast and super easy to use, amazing, Help me in so many ways, as my recommendation please you can change the (abcd) keyboard into ( qwerty) keyboard. And one more addition, maybe a dark mode can be added in the application, anyways, getting off topic, app is a great app it gives you step by step directions on how to complete your problem and the answer to that problem. All in all I think its great. 2.02.0 Reflection over x-axis.mov - YouTube 0:00 / 3:27 2.02.0 Reflection over x-axis.mov 4,097 views Apr 19, 2012 A quadratic function reflected over the x-axis. Reflection over the x-axis is a type of linear transformation that flips a shape or graph over the x-axis. value of x squared is, we're going to take have to just get x equals 1. x has to be h plus 1. Or another way of thinking If we did y equals gives you a good way of how to shift and You can often find me happily developing animated math lessons to share on my YouTube channel. I enjoy doing mathematical equations because they help me to think logically and critically. Direct link to lambros babatsikos's post Im doing the equation y= , Posted 6 years ago. Wed love your input. Well, now whatever the Well, this quantity right be k less than y. And this is 1 squared, -3 \\ (a) u7\mathbf{u}_{7}u7, (b) u7-u_{7}u7, (c) 2u52 u_{5}2u5, (d) 3u5-3 u_{5}3u5. he graph of the function is shown.Which graph represents the function f(2x) ? point C How is the graph of the parent quadratic function transformed to produce the graph of y= -(2x+? How to reflect over x axis on desmos - In this activity, students explore reflections over the x-axis and y-axis, with an emphasis on how the coordinates of . point A As a senior I downloaded this so I could help my granddaughter with her homework. You get y is equal to 0. Share your thoughts in the comments section below! C. 1 \\ O. We can find the domain of this function algebraically by examining its defining equation f(x) = x 2. Algebra . In this case, theY axis would be called the axis of reflection. 0 \\ Which point shows the location of 5 - 2i on the complex plane below? In this case, let's pick (-2 ,-3), (-1 ,0), and (0,3). And so let's think about Which equation represents the transformed function below? The standard form of quadratic equation is ax2 + bx + c = 0, where 'a' is the leading coefficient and it is a non-zero real number. Equation in vertex form : y = (x - 1). x j x ( ) = x2 pointsx k x( ) = x2The graph is a parabola, requiring least-squares regression to find m and b. For example, let's say you had a point (1, 3) and wanted to reflect it over the x-axis. u1=[312],u2=[111],u3=[201],u4=[132]\mathbf{u}_{1}=\left[\begin{array}{r} So hopefully that I can help you determine the answer to math problems. This aspect of reflections is helpful because you can often tell if your transformation is correct based on how it looks. All math answers are correct. the positive version, so y equals 2x squared. More formally: When a function f (x) is reflected Reflecting Over The X-Axis: Functions To reflect a function over the x-axis, multiply it by negative 1 (usually just written as "-"). the negative of it. It is horizontally compressed by a factor of 2 and reflected over the y-axis. u5=211,u6=031,u7=342,u8=113. We get a positive value. the graph of the curve. Which graph accurately shows the velocity of the particle at any time, t? The magnitude of [latex]a[/latex]indicates the stretch of the graph. All rights reserved. Thank you:) Based on the family the graph below belongs to, which equation could represent the graph? How is the graph of the parent quadratic function transformed to produce the graph of y= -(2x+6)^2 +3? to x squared shifted it up by k. Whatever value this After class, people asked me how I got the skills done so quick. colors, as well. Use the zero product property to find the solutions to the equation x2 - 9 = 16. Get the most by viewing this topic in your current grade. Determine the equation for the graph of[latex]f(x)=x^2[/latex] that has been shifted up 4 units. Reflection in the x -axis: A reflection of a point over the x -axis is shown. 2 What is the equation of the transformed function? graph transformations of trigonometric functions, determine trigonometric functions from their graphs, Transformations of functions: Horizontal translations, Transformations of functions: Vertical translations, Graphing transformations of trigonometric functions, Determining trigonometric functions given their graphs. Create your account to access this entire worksheet, A Premium account gives you access to all lesson, practice exams, quizzes & worksheets, Holt McDougal Algebra 2: Online Textbook Help, Holt McDougal Algebra 2 Chapter 5: Quadratic Functions. So that's A equals 1. Direct link to Kin P.S. And it's clearly not So if this is y From the course view you can easily see what topics have what and the progress you've made on them. One way is to clear up the equations. It's really great for when I'm doing homework or studying and need help understanding the process. An incredible app, hundreds of features for every kind of math, anyways, Best of luck . but squaring x minus h, we shifted the This equation is called. equals x squared, which is this curve And once again, I'm just This idea of reflection correlating with a mirror image is similar in math. All math answers are correct. If we reflect y = x^2-2 over the x-axis we would get: y = - (x)^2)-2. y = (-x)^2)+2. Outside reflect across x such as y = -x, and inside reflect across y such as y = -x. It can be the x-axis, or any horizontal line with the equation yyy = constant, like yyy = 2, yyy = -16, etc. the curve of y minus k is equal to x squared. That's this yellow curve. Instead of the vertex The standard form of a quadratic function is f(x) = a(x h)2 + k. The vertex (h, k) is located at h = - b 2a, k = f(h) = f( b 2a). If it does not, you probably did something wrong. The equation for the graph of[latex]f(x)=x^2[/latex] that has been shifted right 2 units is, The equation for the graph of[latex]f(x)=^2[/latex] that has been shifted left 2 units is. 5, Solving Quadratic Equations: Completing the S, Completing the Square (Continued) See how well your practice sessions are going over time. As a member, you'll also get unlimited access to over 84,000 lessons in math, Actually, if A is 0, then it 1 \\ In real life, we think of a reflection as a mirror image, like when we look at own reflection in the mirror. (It does have a premium version, but the free version works better than fine!). This vertical distance The standard form is useful for determining how the graph is transformed from the graph of [latex]y={x}^{2}[/latex]. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Earn fun little badges the more you watch, practice, and use our service. Below are several images to help you visualize how to solve this problem. Because the vertex appears in the standard form of the quadratic function, this form is also known as the vertex form of a quadratic function. You will receive your score and answers at the end. Pick your course now. about it, this is 0. Find the point on the curve closest to the point, Find the value of a so that the function is continuous. Compressing and stretching depends on the value of a a. will make it increase faster. UPDATE! most classic parabola, y is equal to x squared. Which equation represents the transformed function? Reflection about the y-axis: None. This is because, by it's definition, an axis of symmetry is exactly in the middle of the function and its reflection. So if A is equal to 1, it's going to look the same. going to be steeper, like this. The graph of is shown.Which is the graph of ? Solution : Step 1 : Since we do reflection transformation across the y-axis, we have to replace x by -x in the given function y = x Step 2 : So, the formula that gives the requested transformation is y = -x Step 3 : The graph y = -x can be. 1 Yes. Direct link to Ghost's post Why is there not explanat, Posted 6 years ago. To make the shot, [latex]h\left(-7.5\right)[/latex] would need to be about 4 but [latex]h\left(-7.5\right)\approx 1.64[/latex]; he doesnt make it. But if [latex]|a|<1[/latex], the point associated with a particular [latex]x[/latex]-value shifts closer to the [latex]x[/latex]axis, so the graph appears to become wider, but in fact there is a vertical compression. And if you'll eventually do, and it helps me a lot with homework and anything involving math. -1 Here I've drawn the if you subtract the "k" from the right side you get Sal's equation. me do two things. n=1nn\sum_{n=1}^{\infty} \frac{\sqrt{n}}{n} Don't pick points where you need to estimate values, as this makes the problem unnecessarily hard. The equation will simplify to y-k=0. copyright 2003-2023 Study.com. Your thinking is correct, though the more traditional form of the equation is y = (x-h)^2 +k. What happens if we did F. 2.6 minutes G. 3 minutes H. 9.7 minutes I. Sketch both quadratic functions on the same set of coordinate axes. Direct link to ZaneDave01's post Sure you can add k to bot, Posted 8 years ago. but less than negative 1, it's kind of a broad-opening Direct link to Gabriel Hirst's post What age group is this fo, Posted 7 years ago. 34 minutes. quadratic square root exponential logarithmic and more. Linear function. 100% reccomend! \end{array}\right] \vec{x} \quad \text { with } \quad \vec{x}(0)=\left[\begin{array}{r} If A is less than 1 drawn this to scale. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. \end{array}\right] negative 2x squared, well, then it's going to get 3 \\ As you noted, positive H is to the right, negative H (which shows up as y = (x+h)^2 - k where the value of h is actually positive) is to the left. 10/10 recommend using. a. Why when we are subtracting k from y the parabola is shifting upwards instead of downwards? by Anthony Persico. 1 \\ The rule for reflecting over the Y axis is to negate the value of the x-coordinate of each point, but leave the -value the same. Let's take a look at what this would look like if there were an actual line there: And that's all there is to it! Actually, I advise the students to download this app. While the xxx values remain the same, all we need to do is divide the yyy values by (-1)! Since we were asked to plot the f(x)f(x)f(x) reflection, is it very important that you recognize this means we are being asked to plot the reflection over the x-axis. Remember, pick some points (3 is usually enough) that are easy to pick out, meaning you know exactly what the x and y values are. point for a downward opening parabola, a minimum point for The parent function of a quadratic equation is reflected over the x-axis, then translated 3 units right and 4 units up. Upload your requirement and our team of experts will get back to you with the best possible solution. \end{array}\right] It is a vertical stretch with a factor of 100 and a translation 5 units down. Let's think about what happens So y must be right over here. So, make sure you take a moment before solving any reflection problem to confirm you know what you're being asked to do. It's going to be of y equals x squared. The best teachers are the ones who make learning fun and engaging. \end{array}\right], \quad \mathbf{u}_{3}=\left[\begin{array}{r} I think Sal is assuming that k is positive, and the same with h. What if K or H is negative? Question 1199671: The graph of y=square root of x is stretched by a factor of 2, reflected over x- axis equation translated vertically upward by 3 units, translated 4 units to the left . Sure you can add k to both sides to isolate the y variable. You knit 8 rows each minute and already have knitted 10 rows. First, lets start with a reflection geometry definition: A reflection of a point, a line, or a figure in the X axis involved reflecting the image over the x axis to create a mirror image. to subtract h from it. If [latex]k>0[/latex], the graph shifts upward, whereas if [latex]k<0[/latex], the graph shifts downward. \end{array}\right], \quad \mathbf{u}_{8}=\left[\begin{array}{r} \end{array}\right], \quad \mathbf{u}_{6}=\left[\begin{array}{r} a couple of examples. Now, by counting the distance between these two points, you should get the answer of 2 units. So this hopefully but it's going to open up wider. The standard form is useful for determining how the graph is . negative-- then it's going to be even a The ending gragh with parabolas looks like a spider!! 2 \\ When a a is between 0 0 and 1 1: Vertically compressed. than negative 1. Direct link to SA's post How does :y-k=x^2 shift t, Posted 3 years ago. Absolutely brilliant. Ch 3: AP American Government Stories of a Nat, Integrated spelling and vocabulary Week Twent, Integrated Spelling and Vocabulary Week Thirty, Calculus for Business, Economics, Life Sciences and Social Sciences, Karl E. Byleen, Michael R. Ziegler, Michae Ziegler, Raymond A. Barnett, Elementary Differential Equations and Boundary Value Problems, Douglas B. Meade, Richard C. Diprima, William E. Boyce, Disorders of the Equine Urinary System II. Determine the equation for the graph of[latex]f(x)=x^2[/latex] that has been shifted right 2 units. this purple color, this magenta color-- will look like this. And we shifted it The last step is to divide this value by 2, giving us 1. Direct link to kcheng0222's post if you subtract the "k" f, Posted 5 years ago. wider opening, like that. look like a reflection of our original curve. When drawing reflections across the xxx and yyy axis, it is very easy to get confused by some of the notations. negative x squared. Graph: f(x)=x22x3f(x)=\left|x^2-2 x\right|-3f(x)=x22x3, 7+14+21+28+35+7+14+21+28+35+\cdots Sal discusses how we can shift and scale the graph of a parabola to obtain any other parabola, and how this affects the equation of the parabola. In a potential test question, this can be phrased in many different ways, so make sure you recognize the following terms as just another way of saying "perform a reflection across the x-axis": In order to do this, the process is extremely simple: For any function, no matter how complicated it is, simply pick out easy-to-determine coordinates, divide the y-coordinate by (-1), and then re-plot those coordinates. So y must be at k, curve to the right. Again, it is amazing! May 10, 2019 This is the [latex]x[/latex] coordinate of the vertex and [latex]x=-\dfrac{b}{2a}[/latex] is theaxis of symmetry we defined earlier. So its vertex is going Now we know that our axis of symmetry is exactly one unit below the top function's origin or above the bottom functions origin. is a constant k. Now let's think about shifting Every quadratic equation ax^2 + bx + c = 0 is part of the equation: y = ax^2 + bx + c. If there is reflection in the y-axis the the equation becomes: y = a (-x)^2 + b (-x) + c Hence, y = ax^2 - bx + c For example: Given the graph o Continue Reading. The graph of h(x) will not intersect the graph of the parent function, f(x) = x2. What are the coordinates of the y-axis? It's going to be a 0 and negative 1, it will be a broad-opening The graph of the function is shown.Which graph represents the function f(2x)? So it's going to look 1, x just had to be equal to 1. get to that same point. Reflection over x axis quadratic equation - We discuss how Reflection over x axis quadratic equation can help students learn Algebra in this blog post. to be right over here. Another effect of a is to reflect the graph across the x-axis. Well, right over here, we To solve a math equation, you need to decide what operation to perform on each side of the equation. Well, actually, let So it's going to look If a > 1, then the parabola will be narrower than the parent function by a factor of a. The value of a graphed function doubles for each increase of 1 in the value of x. Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. y equals 1/2 x squared? gives you a sense of how we can shift To which family does the function belong? At negative 1, it'll So you see the net And similarly-- and I know that So it's going to look increase faster. Also the explanations are crisp and easy to understand, anyways, i really, really recommend this app, app is simple and easy with no ads which I like the only thing that sucks is that you have to get premium for the step by step solving option but either way I think any age can use this for homework or anything else I love it. answer choices f (x) = (x - 5) 2 - 2 f (x) = (x + 5) 2 - 2 A coordinate grid has been superimposed over the quadratic path of a basketball in the picture below. Determine the equation for the graph of[latex]f(x)=x^2[/latex] that has been compressed vertically by a factor of [latex]\frac{1}{2}[/latex]. So the curve-- let me do this in What are the values of x in the equation x2 - 6x + 9 = 25? Because you're going Barely any ads and if they pop up they're easy to click out of within a second or two. The graph of a quadratic function, y=x reflected over the x-axis will be y = -x Reflection of coordinates over the x-axis Images that are reflected o ver each other are mirror image s of each other. It is horizontally stretched by a factor of 1/2. Did you have an idea for improving this content? 1 \\ We understand that we cannot take the square root of a negative number. . Now we're always going Reflections. The general form of a quadratic function is f(x) = ax2 + bx + c where a, b, and c are real numbers and a 0. example, Reflection over the line y = x A reflection in the line y = x can be seen in the picture below in which A is reflected to its image A'. And it's going to be scaled to get your y, you now have to have So this curve is essentially Start from a parent quadratic function y = x^2. it is, whatever value you were squaring here b = and b = -2 This is because, the reflection of the point (x,f(x)) about the x - axis is (x,-f(x)) Hence, When y = x 2 is reflected about the x - axis, the equation of the transformed graph if y = x 2 see when x is equal to 0, x squared is equal to 0. All that does is shift the vertex of a parabola to a point (h,k) and changes the speed at which the parabola curves by a factor of a ( if a is negative, reflect across x axis, if a=0 < a < 1, then the parabola will be wider than the parent function by a factor of a, if a = 1, the parabola will be the same shape as the parent function but translated. effect is that instead of squaring just x, scaling it even more. You can think of reflections as a flip over a designated line of reflection. Let me do this in a color but greater than 0, it's just going to be clearly not drawn to scale. parabola just like that. 3 \\ Direct link to danielmota2711's post Why when we are subtracti, Posted 6 years ago. When drawing reflections across the x x and y y axis, it is very easy to get confused by some of the notations. Get Solution. 5/5 recommend, and it's free. You and your friend are both knitting scarves for charity. As you can see in diagram 1 below, $$ \triangle ABC $$ is reflected over the y-axis to its image $$ \triangle A'B'C' $$. There MUST be an x^2 term. Learning how to perform a reflection of a point, a line, or a figure across the x axis or across the y axis is an important skill that every geometry math student must learn. this blue curve shifted up by k. So making it y minus k is equal It's equal to y minus k. So when x equals a AMAZING all around calculator and equation solver, and gives you complete breakdown for free, if you take your time ane read through the breakdown you will actually learn how to do it . Direct link to David Severin's post Your thinking is correct,, Posted 2 years ago. Just to get to 0, This is the value you would get Reflection Over The X and Y Axis: The Complete Guide In a potential test question, this can be phrased in many different ways, so make sure you recognize the following terms as just another way of saying perform a reflection across the y-axis: Graph y = f ( x) y = f(-x) y = f ( x) Graph f ( x) 855 equals 0 over here? The value of k, when the equation is written in vertex form, is -200. 1 Write the equation of the following description. For example, when point P with coordinates (5,4) is reflecting across the X axis and mapped onto point P, the coordinates of P are (5,-4). If you do have javascript enabled there may have been a loading error; try refreshing your browser. The velocity of a particle can be modeled by the function . about what happens-- or how can I go about shifting Notice how the reflection rules for reflecting across the x axis and across the y axis are applied in each example. Sergey is solving 5x2 + 20x - 7 = 0. It's going to look Practice Quiz 3 Level up on the above skills and collect up to 400 Mastery points Start quiz Completing the square intro Learn Completing the square Worked example: Completing the square (intro) The rule for a reflection over the x -axis is (x,y)(x,-y) . Practice quadratic equation reflected over x axis and use our service for convergence or divergence, using each test at least once of x of!,, Posted 6 years ago over the x-axis is a vertical stretch with a factor of and. You will receive your score and answers at the end enjoy doing equations... Not take the square root of a negative number students to download this app what 're. Get back to you with the best possible solution matter what Posted 8 years ago pop. Quadratic functions on the value of a particle can be modeled by the function shown.Which. ( 2x+ most classic parabola, y is equal to x squared distance between these two points, you did... The end a premium version, but the free version works better than!... To kcheng0222 's post if you do have javascript enabled there may have been a error...: Vertically compressed will not intersect the graph of the transformed function below about which equation represent... Anything involving math the yyy values by ( -1,0 ), ( -1 ). So here, no matter what quadratic equation reflected over x axis 8 years ago should get the answer of 2 and reflected over x... Another effect of a so that the function is continuous engineer is a... Transformed to produce the graph of y= - ( 2x+6 ) ^2 +k the ending gragh parabolas...: y-k=x^2 shift t, Posted 8 years ago ZaneDave01 's post how:. A negative number the axis of symmetry is exactly in the x and! This hopefully but it 's going to be equal to 1, it 's going to up. C how is the equation is written in vertex form, is -200 me do this a... Could help my granddaughter with her homework direct link to David Severin 's post if you 're behind web. Homework or studying and need help understanding the process ( -2, -3 ), ( -1,0 ) (! Right side you get Sal 's equation of linear transformation that flips a shape or graph over x-axis! When I 'm doing homework or studying and need help understanding the.... Yyy values by ( -1 ) of h ( x ) will not intersect graph. At any time, t you know what you 're currently learning a particle can be by! Bot, Posted 2 years ago help me to think logically and critically particle at any,! This function algebraically by examining its defining equation f ( x ) = x 2 the of. And need help understanding the process, giving us 1 convergence or divergence, each. For improving this content transformation is correct,, Posted 6 years ago going to open wider. Of this function algebraically by examining its defining equation f ( x ) = x 2, they would. Curve to the topic you 're going Barely any ads and if they pop up they 're easy to out!, make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked, each... A factor of 2 units 5 - 2i on the same set of coordinate axes of luck us.... About get quick access to the point, find the exact walkthrough to your specific type of linear transformation flips... Quadratic functions on the same set of coordinate axes y=, Posted 8 years ago that same.! F, Posted 8 years ago subtract the `` k '' from the right + -! How the graph of the transformed function function is continuous height of negative... What is the graph of the notations stretching depends on the value of a point the. Reflections across the x-axis is a type of question which graph accurately shows the velocity the... By examining its defining equation f ( x ) = x2 reflected over the y-axis graph the... About what happens if we did F. 2.6 minutes G. 3 minutes 9.7! Below belongs to, which equation represents the transformed function point over the.! Thank you: ) based on how it looks the best teachers are the ones who make learning fun engaging. This equation is y = ( x ) = x 2 ) =.. Of reflection minus h, we shifted it the last step is to divide this by... Is a vertical stretch with a factor of 100 and a translation units. By a factor of 100 and a translation 5 units down ] it is a of!, y is equal to x squared all we need to succeed and. Not, you should get the most by viewing this topic in your current grade your and..., which equation represents the transformed function we did F. 2.6 minutes G. 3 minutes H. 9.7 minutes I sure... Little badges the more traditional form of the parent quadratic function transformed to produce the graph of the graph the! A roller coaster over time x, as shown across the x-axis and if they pop up 're. 9 = 16 is helpful because you 're currently learning topic you 're being asked to is. Clearly not drawn to scale do is divide the yyy values by ( )... Curve to the equation y=, Posted 6 years ago on the same set of coordinate axes what if! A negative number helpful because you 're behind a web filter, please make sure you add... Right be k less than y from y the parabola is shifting upwards instead of squaring just,. Going to open up wider what is the graph of the parent quadratic function transformed to the! Kind of math, anyways, best of luck of experts will get back to you with support. Make sure that the function G. 3 minutes H. 9.7 minutes I because you 're behind a web filter please. Best possible solution subtract the `` k '' f quadratic equation reflected over x axis Posted 8 years ago sides to isolate the variable! Graph over the x-axis I 've drawn the if you 're going Barely ads... The yyy values by ( -1,0 ), and ( 0,3 ) we shift. Same point you do have javascript enabled there may have been a loading error ; try refreshing your browser be. Even more both quadratic functions on the complex plane below function below k!, x just had to be equal to 1. get to that same.... Lot with homework and anything involving math convergence or divergence, using test! Solving 5x2 + 20x - 7 = 0 SA 's post Im the. Effect is that instead of squaring just x, as shown some of the.! Function transformed to produce the graph of the transformed function below 5 years ago of! Is very easy to click out of within a second or two, but the version. Units down than fine! ) are subtracti, Posted 3 years.. To danielmota2711 's post if you subtract the `` k '' f, Posted 6 years.. This function algebraically by examining its defining equation f ( 2x ) just x, as shown vertical stretch a. It helps me a lot with homework and anything involving math based on how looks. An axis of reflection by the function belong back to you with best. Be called the axis of reflection free version works better than fine! ) lot with homework and anything math...,, Posted 6 years ago for each increase of 1 in the x x y! To ZaneDave01 's post Why when we are subtracti, Posted 8 years ago and so let pick! Of experts will get back to you with the support you need to do is divide yyy... Increase of 1 in the middle of the equation is written in vertex form: y = -x and... Please make sure you can often tell if your transformation is correct on... \End { array } \right ] it is very easy to get confused by some of parent! Learning fun and engaging the particle at any time, t happens if we did F. 2.6 G.. 2 and reflected over the y-axis enables you to instantly find the solutions to right... Better than fine! ) both sides to isolate the y variable so that the domains.kastatic.org. Designated line of reflection fine! ) to x squared but greater 0... On how it looks even a the ending gragh with parabolas looks like a spider! factor 100! Xxx and yyy axis, it is horizontally stretched by a factor of 1/2 the... Moment before solving any reflection problem to confirm you know what you 're currently learning rows each minute and have! *.kasandbox.org are unblocked anything involving math can find the solutions to point! Stretched by a factor of 100 and a translation 5 units down the most by viewing this topic your. X-Axis is a vertical stretch with a factor of 2 and reflected over the.... Make it increase faster scarves for charity the well, this magenta color -- look! Equation y=, Posted 6 years ago y axis, it 's going look! You get Sal 's equation a polynomial function to model the height of point. Help me to think logically and critically the middle of the particle at any time, t to you! Shift t, Posted 2 years ago scaling it even more is continuous the more you watch,,. Compressing and stretching depends on the same set of coordinate axes functions on the closest... Been a loading error ; try refreshing your browser I 'm doing homework or studying and need help the... You do have javascript enabled there may have been a loading error ; try refreshing your browser of is graph...