# How do you graph quadratic equations written in vertex form?

Jul 25, 2018

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#### 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

$y = {\left(0 - 3\right)}^{2} + 8$

$y = 9 + 8$

$y = 17$

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

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

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

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

$\Rightarrow x = 3$

We can verify this from the graph below:

Hope it helps.