Section 3.3 Quadratic Functions

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Section 3.3Quadratic Functions
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A quadratic function is a function of the form
where a, b, and c are real numbers and a
0. The domain of a quadratic function consists
of all real numbers.
The graph of a quadratic function is called a
parabola.
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Graphs of a quadratic function f(x) ax2 bx
c, a 0
Vertex is highest point
Axis of symmetry
Axis of symmetry
Vertex is lowest point
a lt 0
a gt 0
Opens up
Opens down
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Now use the methods of Chapter 2 to Graph.
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Vertex (2,7)
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Properties of the Quadratic Function
Parabola opens up if a gt 0. Parabola opens down
if a lt 0.
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Given the function ,
determine whether the graph opens upward or
downward. Find the vertex, axis of symmetry, the
x-intercepts, and the y-intercept.
x-coord. of vertex
y-coord. of vertex
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y-intercepts f(0) 5 so the y-intercept is
(0,5)
x-intercepts Solve the equation
0
The x-intercepts are approximately (-5.6,0) and
(-.45,0)
Summary Parabola opens up Vertex (-3,
-13) y-intercept (0,5) x-intercepts (-0.45,
0) and (-5.55,0)
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Now, graph the function using the information
found in the previous steps.