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

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WORKSHEET 8.13: DESCRIBING THE GRAPH OF THE
QUADRATIC FUNCTION
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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


.


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


in the equation and solve fory.


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

  2. 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.

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©


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

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