Quadratic Functions

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Quadratic Functions
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A quadratic function is a function of the form
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Properties of the Graph of a Quadratic Function
Parabola opens up if a gt 0 the vertex is a
minimum point. Parabola opens down if a lt 0 the
vertex is a maximum point.
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Graphs of a quadratic function f(x) ax2 bx c
Vertex is highest point
Axis of symmetry
Axis of symmetry
a gt 0
a lt 0
Opens up
Opens down
Vertex is lowest point
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Graph the parabola
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The graph of is a parabola with
vertex (0, 0)
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Locate the vertex and find the axis of symmetry
of the following parabola. Does it open up or
down? Graph the parabola.
Vertex
Since -3 lt 0 the parabola opens down.
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Determine whether the graph opens up or
down. Find its vertex and axis of symmetry. Graph
the parabola.
x-coordinate of vertex
y-coordinate of vertex
Axis of symmetry
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Use the graph of to sketch the
graph of
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• By completing the square the equation
• Can be written in the form

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The standard form of the equation of a parabola
Vertex (h, k) Parabola opens up if a is
positive Parabola opens down if a is negative
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Write the equation
in standard form.
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Graph the function
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vertex (2, 13) Parabola opens down since a is
negative
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Vertex
(2, 13)