How do you graph quadratic equations written in vertex form?

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Answer 1 · 2018-07-25T04:27:14

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Please read the explanation.

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Quadratic Equations in Vertex Form have a general form:

$color(red)(y=f(x)=a(x-h)^2+k$ , where

$color(red)((h,k)$ is the $color(blue)("Vertex"$

Let us consider a quadratic equation in Vertex Form:

$color(blue)(y=f(x)=(x-3)^2+8$ , where

$color(green)(a=1; h=3; k=8$

Hence, $color(blue)("Vertex "= (3, 8)$

To find the y-intercept, set $color(red)(x=0$

$y=(0-3)^2+8$

$y=9+8$

$y= 17$

Hence, the y-intercept: $color(blue)((0, 17)$

We can use a table of values to draw the graph:

enter image source here

Use the table with two columns $color(red)(x and y$ to draw the graph as shown below:

enter image source here

The Parent Graph of $color(red)(y=x^2$ can also be seen for comparison, to better understand transformation.

Also note that,

**Axis of Symmetry is ** $color(red)(x=h$

$rArr x= 3$

We can verify this from the graph below:

enter image source here

Hope it helps.