how to stretch a parangula
February 2016

A horizontal reflection is given by the equation [latex]y = f(-x)[/latex] and results in the curve being “reflected” across the y-axis.

February 2015 December 2018 ", with understanding the concept. A horizontal reflection is a reflection across the [latex]y[/latex]-axis, given by the equation: In this general equation, all [latex]x[/latex] values are switched to their negative counterparts while the y values remain the same. August 2015

December 2017 February 2014 Parabolas are also symmetrical which means they can be folded along a line so that all of the points on one side of the fold line coincide with the corresponding points on the other side of the fold line. CC licensed content, Specific attribution,,,,,,, December 2016 D.) y = -0.75x² A parabola is stretched away from the x-axis, thus making it more narrow, by multiplying the y-value by a number greater than 1. To translate a function vertically is to shift the function up or down. Please help us continue to provide you with our trusted how-to guides and videos for free by whitelisting wikiHow on your ad blocker. Thank you. Therefore, we can say that [latex]f(-x)[/latex] is a reflection of [latex]f(x)[/latex] across the [latex]y[/latex]-axis. September 2013

The positive numbers on the y-axis are above the point (0, 0), and the negative numbers on the y-axis are below the point (0, 0). Use the quadratic function to learn why a parabola opens wider, opens more narrow, or rotates 180 degrees.

As an example, let [latex]f(x) = x^3[/latex]. These translations shift the whole function up or down the y-axis. Graph of a function being translated: The function [latex]f(x)=x^3[/latex] is translated by two in the positive [latex]y[/latex] direction (up). This is no different from any other parabola.

[beautiful math coming... please be patient] y =f(x k) y = f ( x k) . December 2015

Therefore the horizontal reflection produces the equation: [latex]\displaystyle \begin{align} y &= f(-x)\\ &= (-x-2)^2 \end{align}[/latex]. Put arrows at the ends. Let the function in question be [latex]f(x) = x^5[/latex]. As an example, let the original function be: The reflected equation, as reflected across the line [latex]y=x[/latex], would then be: Reflection over [latex]y=x[/latex]: The function [latex]y=x^2[/latex] is reflected over the line [latex]y=x[/latex]. To make a table, simply choose a value for x, such as 0, and plug it into the original equation to solve for y. July 2020 November 2014 January 2012 February 2017 November 2015 February 2012

We use cookies to make wikiHow great. Any point on the parabola is equidistant from a fixed point (the focus) and a fixed straight line (the directrix). A translation moves every point in a function a constant distance in a specified direction.

If [latex]b>1[/latex], the graph stretches with respect to the [latex]y[/latex]-axis, or vertically. Common types of transformations include rotations, translations, reflections, and scaling (also known as stretching/shrinking). X In order to graph a parabola, you need to find its vertex as well as several points on either side of the vertex in order to mark the path that the points travel. Jake holds a BA in International Business and Marketing from Pepperdine University. Horizontal translation: The function [latex]f(x)=x^2[/latex] is translated both left and right by two. June 2015 February 2013 In general, a vertical translation is given by the equation: [latex]\displaystyle y = f(x) + b[/latex]. Thanks to all authors for creating a page that has been read 166,475 times. [7]

This change will cause the graph of the function to move, shift, or stretch, depending on the type of transformation. In this case the axis of symmetry is x = 0 (which is the y-axis of the coordinate plane). To translate a function horizontally is the shift the function left or right.

If the function [latex]f(x)[/latex] is multiplied by a value less than one, all the [latex]y[/latex] values of the equation will decrease, leading to a “shrunken” appearance in the vertical direction. The reflection of a function can be performed along the [latex]x[/latex]-axis, the [latex]y[/latex]-axis, or any line. Points on it include (-1, 1), (1, 1), (-2, 4), and (2, 4). How do I find the formula for a given parabola?

[1] The result is that the curve becomes flipped over the [latex]x[/latex]-axis. A transformation takes a basic function and changes it slightly with predetermined methods. Multiplying the independent variable [latex]x[/latex] by a constant greater than one causes all the [latex]x[/latex] values of an equation to increase.

A vertical reflection is a reflection across the [latex]x[/latex]-axis, given by the equation: In this general equation, all [latex]y[/latex] values are switched to their negative counterparts while the [latex]x[/latex] values remain the same. Thus, dividing the input by a constant stretches the function in the x direction, and multiplying the input by a constant shrinks the function in the x direction. Other sites didn't explain it in a way I understood, but this explained thoroughly how to do it, and it made sense!


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