10.4 Solving Quadratic Equations in Factored Form

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Presentation transcript:

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. 1/18/2019 10.4 Solving Quadratic Equations in Factored Form

10.4 Solving Quadratic Equations in Factored Form Ex. 1. Solve the equation. (x-2)(x-3)=0 x-2 = 0 x-3 = 0 +2 +2 +3 +3 x=2 x=3 Process: Set each factor equal to zero Solve 1/18/2019 10.4 Solving Quadratic Equations in Factored Form

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 -1 -1 +3 +3 x=-1 x=3 b. x(x-2)=0 x= 0 x-2 = 0 +2 +2 x=2 c. (x-5)(x+7)=0 x-5 = 0 x+7 = 0 +5 +5 -7 -7 x=5 x=-7 d. (x-4)(x+1)=0 x-4= 0 x+1 = 0 +4 +4 -1 -1 x=4 x=-1 1/18/2019 10.4 Solving Quadratic Equations in Factored Form

10.4 Solving Quadratic Equations in Factored Form Ex. 3. Solve the equation. a. (x+5)2=0 x+5 = 0 x+5 = 0 -5 -5 -5 -5 x=-5 x=-5 b. (x+8)2=0 x+8 = 0 -8 -8 x=-8 c. (x-4)2=0 x-4 = 0 +4 +4 x=4 d. (x+6)2=0 x+6 = 0 -6 -6 x=-6 1/18/2019 10.4 Solving Quadratic Equations in Factored Form

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 -1 -1 +2 +2 +1 +1 2x=-1 3x=+2 x=1 2 2 3 3 x=-1/2 x=2/3 b. (3x-2)(4x+3)(x+4)=0 3x-2=0 4x+3=0 x+4 = 0 +2 +2 -3 -3 -4 -4 3x=2 4x=-3 x=-4 3 3 4 4 x=2/3 x=-3/4 1/18/2019 10.4 Solving Quadratic Equations in Factored Form

10.4 Solving Quadratic Equations in Factored Form Ex. 5. Solve the equation. a. (x-4)(x+6)(4x+3)=0 x-4=0 x+6=0 4x+3 = 0 +4 +4 -6 -6 -3 -3 x=4 x=-6 4x=-3 4 4 x=-3/4 b. (x-3)(3x+2)(x+6)=0 x-3=0 3x+2=0 x+6 = 0 +3 +3 -2 -2 -6 -6 x=3 3x=-2 x=-4 3 3 x=-2/3 1/18/2019 10.4 Solving Quadratic Equations in Factored Form

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 -1 -1 +8 +8 2x=-1 x=8 2 2 x=-1/2 b. (x-3)2(3x-2)=0 x-3=0 3x-2=0 +3 +3 +2 +2 x=3 3x=2 3 3 3 3 x=2/3 x=2/3 1/18/2019 10.4 Solving Quadratic Equations in Factored Form

10.4 Solving Quadratic Equations in Factored Form Ex. 7. Sketch the graph. y=(x-3)(x+2) x-3=0 x+2=0 +3 +3 -2 -2 x=3 x=-2 x-coord=3+-2 = 1 2 2 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 1/18/2019 10.4 Solving Quadratic Equations in Factored Form

10.4 Solving Quadratic Equations in Factored Form Ex. 8. Sketch the graph. y=(x-4)(x+2) x-4=0 x+2=0 +4 +4 -2 -2 x=4 x=-2 x-coord=4+-2 = 2=1 2 2 y-coord=(1-4)(1+2) =(-3)(3) =-9 Vertex: (1, -9) 1/18/2019 10.4 Solving Quadratic Equations in Factored Form

10.4 Solving Quadratic Equations in Factored Form Ex. 9. Sketch the graph. y=x(x+2) x=0 x+2=0 -2 -2 x=-2 x-coord=0+-2 = -2=-1 2 2 y-coord=(-1)(-1+2) =(-1)(1) =-1 Vertex: (-1, -1) 1/18/2019 10.4 Solving Quadratic Equations in Factored Form

10.4 Solving Quadratic Equations in Factored Form Ex. 10. Sketch the graph. y=(x+4)(x-5) x+4=0 x-5=0 -4 -4 +5 +5 x=-4 x=5 x-coord=-4+5 = 1 2 2 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) 1/18/2019 10.4 Solving Quadratic Equations in Factored Form