The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 8.13: DESCRIBING THE GRAPH OF THE

QUADRATIC FUNCTION

-------------------------------------------------------------------------------------

The graph of every quadratic function is a parabola. The equationy=ax^2 +bx+c,a= 0 ,can

be used to describe the vertex and axis of symmetry of the graph. Follow the steps below:

1. Identifyaandb.


2. Determine the sign ofa.Ifais positive, the graph has a minimum point. Ifais negative,
   the graph has a maximum point.


3. Find thex-coordinate of the vertex. Use the formulax=−
   b
   2 a

.

4. Find they-coordinate of the vertex. Substitutex=−
   b
   2 a

in the equation and solve fory.

5. Use thex-andy-coordinates to write the vertex.


6. Find the axis of symmetry. The linex=−

b

2 a

is the axis of symmetry.

EXAMPLE

Describe the graph ofy=x^2 + 4 x− 3.

a= 1 andb= 4.

Becausea> 0, the graph has a minimum point.

Thex-coordinate of the vertex isx=−

4

2 · 1

=− 2.

They-coordinate of the vertex isy=1(−2)^2 +4(−2)− 3 =− 7.

The vertex is (−2,−7).

Theaxisofsymmetryisthelinex=− 2.

DIRECTIONS: Describe the graph of each equation.

1. y=x^2 −x+ 2 2. y=−x^2 − 3 x+ 1


2. y=x^2 − 1 4. y=− 2 x^2 + 6 x− 9

CHALLENGE:Explain why the coefficient of a quadratic equation cannot

equal 0.

299

Copyright

©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.