How do you graph quadratic equations written in vertex form?

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Answer 1 · 2018-07-25T04:27:14

#" "#
Please read the explanation.

#" "#
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.