Quadratic Equations

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Quadratic Equations
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A quadratic equation is an equation of the form
y
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Properties of the Graph of a Quadratic Equation
y
y
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 y 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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Steps for Graphing a Quadratic Equation by Hand

• Determine the axis of symmetry
• Determine the vertex.
• The vertex
• Factor the equation to find the x intercepts
• Find the solution of the factors
• Graph.

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Without graphing, locate the vertex and find the
axis of symmetry of the following parabola. Does
it open up or down?
The Axis Of Symmetry
Vertex is (-1,0)
Since A gt 0 the parabola opens up.
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Find the X intercepts by factoring the Quadratic
The Product is -3 The Sum is 2
The Factors are 3 and -1
Therefore (x3) (x-1) The Solutions are x -3
and x 1
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Graph
Remember When you plot the vertex, it goes on
the Line Of Symmetry!
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(2,4)
(0,0)
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Determine whether the graph opens up or
down. Find its vertex and axis of symmetry.
Axis of Symmetry
y-coordinate of vertex
Vertex (-3,-13)