Name Date
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:
- Identifyaandb.
- Determine the sign ofa.Ifais positive, the graph has a minimum point. Ifais negative,
the graph has a maximum point. - Find thex-coordinate of the vertex. Use the formulax=−
b
2 a
.
- Find they-coordinate of the vertex. Substitutex=−
b
2 a
in the equation and solve fory.
- Use thex-andy-coordinates to write the vertex.
- 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.
- y=x^2 −x+ 2 2. y=−x^2 − 3 x+ 1
- 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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Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.