1. 10.4 Solving Quadratic Equations in Factored Form
Factored Form – written as the product of two or more factors
Zero Product Property – if the product of two factors is zero, then at least one of the factors must be zero.
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10.4 Solving Quadratic Equations in Factored Form

2. 10.4 Solving Quadratic Equations in Factored Form
Ex. 1. Solve the equation.
(x-2)(x-3)=0
x-2 = 0 x-3 = 0
x=2 x=3
Process:
Set each factor equal to zero
Solve
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10.4 Solving Quadratic Equations in Factored Form

3. 10.4 Solving Quadratic Equations in Factored Form
Ex. 2. Solve the equation.
a. (x+1)(x-3)=0
x+1 = 0 x-3 = 0
x= x=3
b. x(x-2)=0
x= 0 x-2 = 0
x=2
c. (x-5)(x+7)=0
x-5 = 0 x+7 = 0
x= x=-7
d. (x-4)(x+1)=0
x-4= 0 x+1 = 0
x=4 x=-1
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10.4 Solving Quadratic Equations in Factored Form

4. 10.4 Solving Quadratic Equations in Factored Form
Ex. 3. Solve the equation.
a. (x+5)2=0
x+5 = 0 x+5 = 0
x= x=-5
b. (x+8)2=0
x+8 = 0
x=-8
c. (x-4)2=0
x-4 = 0
x=4
d. (x+6)2=0
x+6 = 0
x=-6
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10.4 Solving Quadratic Equations in Factored Form

5. 10.4 Solving Quadratic Equations in Factored Form
Ex. 4. Solve the equation.
a. (2x+1)(3x-2)(x-1)=0
2x+1=0 3x-2=0 x-1 = 0
2x= x=+2 x=1
x=-1/ x=2/3
b. (3x-2)(4x+3)(x+4)=0
3x-2=0 4x+3=0 x+4 = 0
3x= x=-3 x=-4
x=2/ x=-3/4
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10.4 Solving Quadratic Equations in Factored Form

6. 10.4 Solving Quadratic Equations in Factored Form
Ex. 5. Solve the equation.
a. (x-4)(x+6)(4x+3)=0
x-4= x+6=0 4x+3 = 0
x= x= x=-3
x=-3/4
b. (x-3)(3x+2)(x+6)=0
x-3=0 3x+2=0 x+6 = 0
x= x= x=-4
3 3
x=-2/3
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10.4 Solving Quadratic Equations in Factored Form

7. 10.4 Solving Quadratic Equations in Factored Form
Ex. 6. Solve the equation.
a. (2x+1)(x-8)2=0
2x+1=0 x-8=0
2x= x=8
2 2
x=-1/2
b. (x-3)2(3x-2)=0
x-3=0 3x-2=0
x= x=2
x=2/ x=2/3
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10.4 Solving Quadratic Equations in Factored Form

8. 10.4 Solving Quadratic Equations in Factored Form
Ex. 7. Sketch the graph.
y=(x-3)(x+2)
x-3=0 x+2=0
x=3 x=-2
x-coord=3+-2 = 1
y-coord=(1/2-3)(1/2+2)
=(-2 ½)(2 ½)
=-25/4=-6 ¼
Vertex: (1/2, -6 ¼)
Process:
Find the x-intercepts (set equal to zero)
Find the average – this will be the x-coordinate of the vertex
Substitute into the original to find the y-coordinate
Sketch the graph
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10.4 Solving Quadratic Equations in Factored Form

9. 10.4 Solving Quadratic Equations in Factored Form
Ex. 8. Sketch the graph.
y=(x-4)(x+2)
x-4=0 x+2=0
x=4 x=-2
x-coord=4+-2 = 2=1
y-coord=(1-4)(1+2)
=(-3)(3)
=-9
Vertex: (1, -9)
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10.4 Solving Quadratic Equations in Factored Form

10. 10.4 Solving Quadratic Equations in Factored Form
Ex. 9. Sketch the graph.
y=x(x+2)
x=0 x+2=0
x=-2
x-coord=0+-2 = -2=-1
y-coord=(-1)(-1+2)
=(-1)(1)
=-1
Vertex: (-1, -1)
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10.4 Solving Quadratic Equations in Factored Form

11. 10.4 Solving Quadratic Equations in Factored Form
Ex. 10. Sketch the graph.
y=(x+4)(x-5)
x+4=0 x-5=0
x= x=5
x-coord=-4+5 = 1
y-coord=(1/2+4)(1/2-5)
=(4 1/2)(-4 1/2)
=-81=-20 1/4 4
Vertex: (1/2, -20 1/4)
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10.4 Solving Quadratic Equations in Factored Form