10.7: Vertex Form of a Quadratic Equation
What if you had a quadratic function like
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CK12 Foundation: 1007S Graph Quadratic Functions in Vertex Form
Guidance
Probably one of the best applications of the method of completing the square is using it to rewrite a quadratic function in vertex form. The vertex form of a quadratic function is
This form is very useful for graphing because it gives the vertex of the parabola explicitly. The vertex is at the point
It is also simple to find the
To find the
Example A
Find the vertex, the
a)
b)
Solution
a)
Vertex: (1, 2)
To find the
The solutions are not real so there are
no
To find the
b)
To find the
To find the
To graph a parabola, we only need to know the following information:
 the vertex

the
x− intercepts 
the
y− intercept 
whether the parabola turns up or down (remember that it turns up if
a>0 and down ifa<0 )
Example B
Graph the parabola given by the function
Solution
To find the
To find the
And since
Graph all the points and connect them with a smooth curve:
Example C
Graph the parabola given by the function
Solution:
To find the
Note: there is only one
To find the
Since
Graph all the points and connect them with a smooth curve:
Watch this video for help with the Examples above.
CK12 Foundation: 1007 Graph Quadratic Functions in Vertex Form
Vocabulary
 The vertex form of a quadratic function is
This form is very useful for graphing because it gives the vertex of the parabola explicitly. The vertex is at the point

To find the
x− intercepts from the vertex form: just sety=0 and take the square root of both sides of the resulting equation.

To find the
y− intercept, setx=0 and simplify.
Guided Practice
Graph the parabola given by the function
Solution:
To find the
The
To find the
Since
Graph all the points and connect them with a smooth curve:
Explore More
Rewrite each quadratic function in vertex form.

y=x2−6x 
y+1=−2x2−x 
y=9x2+3x−10 
y=−32x2+60x+10
For each parabola, find the vertex; the

y−4=x2+8x 
y=−4x2+20x−24 
y=3x2+15x 
y+6=−x2+x 
x2−10x+25=9 
x2+18x+81=1 
4x2−12x+9=16 
x2+14x+49=3 
4x2−20x+25=9 
x2+8x+16=25
Intercept
The intercepts of a curve are the locations where the curve intersects the and axes. An intercept is a point at which the curve intersects the axis. A intercept is a point at which the curve intersects the axis.Parabola
A parabola is the characteristic shape of a quadratic function graph, resembling a "U".Vertex
A vertex is a corner of a threedimensional object. It is the point where three or more faces meet.Image Attributions
Description
Learning Objectives
Here you'll learn how to find the vertex, the
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Date Created:
Oct 01, 2012Last Modified:
Jul 31, 2015Vocabulary
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