Aim: How Do We Solve Quadratic Equations by Factoring

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Presentation transcript:

Aim: How Do We Solve Quadratic Equations by Factoring Do Now: Factor: x2+3x-18

Example: Solve. x2+3x-18=0 x2+3x-18=0 Factor the left side (x+6)(x-3)=0 set each factor =0 x+6=0 OR x-3=0 solve each eqn. -6 -6 +3 +3 x=-6 OR x=3 check your solutions!

Example: Solve. 2t2-17t+45=3t-5 2t2-17t+45=3t-5 Set eqn. =0 2t2-20t+50=0 factor out GCF of 2 2(t2-10t+25)=0 divide by 2 t2-10t+25=0 factor left side (t-5)2=0 set factors =0 t-5=0 solve for t +5 +5 t=5 check your solution!

Example: Solve. 3x-6=x2-10 3x-6=x2-10 Set = 0 0=x2-3x-4 Factor the right side 0=(x-4)(x+1) Set each factor =0 x-4=0 OR x+1=0 Solve each eqn. +4 +4 -1 -1 x=4 OR x=-1 Check your solutions!

Solve for x: 3 + x2 – x = 5 x2 – x – 2 = 0 (x – 2)(x + 1) = 0 x = 2, x = –1

Solve for x: 2x2 + 4x = 30 2(x2 + 2x – 15) = 0 x2 + 2x – 15 = 0 (x + 5)(x - 3) = 0 x = -5, x = 3

Solve x2 – 5x = 0. x(x – 5) = 0 x = 0, x = 5 Solve (x – 5)2 – 100 = 0. The left side of the equation is the difference of two squares, then factor it into two binomials [(x – 5) + 10][(x – 5) – 10] = 0 (x +5)(x – 15) = 0 x = -5, x = 15

Solve for x: 2x2 – 4x = 12 + x 2x2 – 5x – 12 = 0 (2x + 3)(x – 4) = 0 2x + 3 = 0, x – 4 = 0 x = 4

You Try It! Solve the following equations: x2 – 25 = 0 x2 + 7x – 8 = 0 c2 – 8c = 0 5b3 + 34b2 = 7b

Finding the Zeros of an Equation The Zeros of an equation are the x-intercepts ! First, change y to a zero. Now, solve for x. The solutions will be the zeros of the equation.

Example: Find the Zeros of y=x2-x-6 y=x2-x-6 Change y to 0 0=x2-x-6 Factor the right side 0=(x-3)(x+2) Set factors =0 x-3=0 OR x+2=0 Solve each equation +3 +3 -2 -2 x=3 OR x=-2 Check your solutions! If you were to graph the eqn., the graph would cross the x-axis at (-2,0) and (3,0).