9.1 Graphing Quadratic Functions and 9.2 Solving Quadratics by Graphing

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9.1 Graphing Quadratic Functionsand9.2 Solving
Quadratics by Graphing

• Assignment 25 9.1 and 9.2 WS 1 17 all

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9.1 Graphing Quadratic Functions2
Graph y 3x2 6x 2.
STEP 1
Determine whether the parabola opens up or down.
Because a gt 0, the parabola opens up.
STEP 2
Find and draw the axis of symmetry
STEP 3
Find and plot the vertex.
The x-coordinate of the vertex is b

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To find the y-coordinate, substitute x in the
function and simplify.
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STEP 4
Example 2
Plot two points. Choose two x-values less than
the x-coordinate of the vertex. Then find the
corresponding y-values.
STEP 5
Reflect the points plotted in Step 4 in the axis
of symmetry.
STEP 6
Draw a parabola through the plotted points.
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9.2 Solving Quadratic Equations by Graphing

• The number of real solutions is at most two.

No solutions
One solution
Two solutions
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Solving Equations

• When we talk about solving these equations, we
  want to find the value of x when y 0. These
  values, where the graph crosses the x-axis, are
  called the x-intercepts.
• These values are also referred to as solutions,
  zeros, or roots.

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Identifying Solutions

• Example f(x) x2 - 4

Solutions are -2 and 2.
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Identifying Solutions

• Now you try this problem.
• f(x) 2x - x2

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Graphing Quadratic Equations

• The graph of a quadratic equation is a parabola.
• The roots or zeros are the x-intercepts.
• The vertex is the maximum or minimum point.
• All parabolas have an axis of symmetry.

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Graphing Quadratic Equations

• One method of graphing uses a table with
  arbitrary
• x-values.
• Graph y x2 - 4x

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Graphing Quadratic Equations

• Try this problem y x2 - 2x - 8.
• Roots
• Axis of Symmetry
• Vertex