Algebra 2 10/11/16 EQ: How do I solve a quadratic by factoring Algebra 2 10/11/16 EQ: How do I solve a quadratic by factoring? HW: pg 338 # 5-17 all, 46-53 all Warm up: What are the roots of a quadratic and what is the equation of a parabola in x intercept(s) form?

Writing an equation in standard form Recall y = a(x-p)(x-q) Write an equation with roots at -4 and 2. y = (x +4) (x-2) y = x2 +4x – 2x -8 y = x2 +2x -8 Question: What happened to a? FOIL Combine like terms

Your Turn Recall y = a(x-p)(x-q) Write 2 equations with roots at 3 and -1.

Solve by Factoring ZERO Recall that the y value of the roots is ________ . Set equations to 0. Factor any like terms (not needed but recommended) Is a = 1 or something else?

a = 1 y = x2 + 9x + 18

a = 1 24 = x2 -2x

Factoring GCF n2 + 5n = 0

y = 2x2 -10x +8

a ≠ 1 3x2 = -x + 4

9x2 +12x +4

Word Problems Find the dimensions of each side A = 50 m2 X - 3 X + 2

Projectile A ball is thrown upwards with an initial velocity of 64ft/s and an initial height of 10 ft. Write an equation that describes the projectile How long is it going to take for the ball to reach 72ft? How many seconds will the ball be above 58ft?

Special Cases Difference of squares (a2 – b2) = (a – b) (a + b) x2 – 25 = 9x2 – 36 = 100x2 – 1= x4 – 49 =

Special Cases (cont.) Perfect Squares a2 + 2ab + b2 = (a + b)2 a2 - 2ab + b2 = (a - b)2 X2 + 6x + 9 = X2 + 10x + 25 = 4x2 – 24x + 36 = OR