Factor and Solve Quadratic Equations

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Factor and SolveQuadratic Equations

• Ms. Nong

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What is in this unit?

• Graphing the Quadratic Equation
• Identify the vertex and intercept(s) for a
  parabola
• Solve by taking SquareRoot Squaring
• Solve by using the Quadratic Formula
• Solve by Completing the Square
• Factor Solve Trinomials (split the middle)
• Factor Solve DOTS difference of two square
• Factor GCF (greatest common factors)
• Factor by Grouping

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• Parts of a Parabola

• The ROOTS (or solutions) of a polynomial are its
  x-intercepts
• Recall The x-intercepts occur where y 0.

Roots X-Intercepts Zeros means the same
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Solving a Quadratic

• The x-intercepts (when y 0) of a quadratic
  function
• are the solutions to the related quadratic
  equation.

• The number of real solutions is at most two.

• One solution
• X 3

• Two solutions
• X -2 or X 2

• No solutions

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Vertex (h,k)

• Maximum point if the parabola is up-side-down
• Minimum point is when the Parabola is UP

agt0
alt0
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All parts labeled
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Can you answer these questions?

• How many Roots?
• Where is the Vertex?
• (Maximum or minimum)
• What is the Y-Intercepts?

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What is in this unit?

• Graph the quadratic equations (QE)
• Solve by taking SquareRoot Squaring
• Solve by using the Quadratic Formula
• Solve by Completing the Square
• Factor Solve Trinomials (split the middle)
• Factor Solve DOTS difference of two square
• Factor GCF (greatest common factors)
• Factor by Grouping

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Finding the Axis of Symmetry
When a quadratic function is in standard form
y ax2 bx c,
the equation of the Axis of symmetry is
This is best read as the opposite of b
divided by the quantity of 2 times a.
Find the Axis of symmetry for y 3x2 18x 7

• The Axis of symmetry is x 3.

a 3 b -18
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Finding the Vertex
The Axis of symmetry always goes through the
_______. Thus, the Axis of symmetry gives us the
____________ of the vertex.
Vertex
X-coordinate
Find the vertex of y -2x2 8x - 3
STEP 1 Find the Axis of symmetry
The x-coordinate of the vertex is 2
a -2 b 8
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Finding the Vertex
Find the vertex of y -2x2 8x - 3
STEP 1 Find the Axis of symmetry
STEP 2 Substitute the x value into the
original equation to find the y coordinate of
the vertex.
The vertex is (2 , 5)
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Graphing a Quadratic Function
STEP 3 Find two other points and reflect them
across the Axis of symmetry. Then connect the
five points with a smooth curve.
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5
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Y-intercept of a Quadratic Function
The y-intercept of a Quadratic function can Be
found when x 0.
The constant term is always the y- intercept
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Example Graph y -.5(x3)24

• a is negative (a -.5), so parabola opens down.
• Vertex is (h,k) or (-3,4)
• Axis of symmetry is the vertical line x -3
• Table of values x y
• -1 2
• -2 3.5
• -3 4
• -4 3.5
• -5 2

• Vertex (-3,4)

• (-4,3.5)

• (-2,3.5)

• (-5,2)

• (-1,2)

• x-3

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Your assignment