Warm Up

y = 8x 2 – 16x -10 = roots a = 8, b = – 16, c = -10 Axis of symmetry = -b 2a x = -(-16) 2(8) = 1 y = 8(1) 2 – 16(1) -10 = -18 Vertex= minimum a > 0 parabola opens up (1, -18) y-intercept Axis of symmetry

y = 4x 2 – 16x + 15 = roots a = 4, b = – 16, c = 15 Axis of symmetry = -b 2a x = -(-16) 2(4) = 2 y = 4(2) 2 – 16(2) +15 = -1 Vertex= minimum a > 0 parabola opens up (2, -1) y-intercept To plot one more point: Select any x and solve for y Ex: when x = 1, y = 4(1) 2 – 16(1) + 15 =3 (1,3) (1,3) (3,3)

0 = 32t – 16t 2

h = 32t – 16t 2 h = – 16t t a < 0 parabola opens down Vertex= maximum (1, 16) At what time will the ball be 8 meters in the air? Axis of symmetry 8 = – 16t t 0 = – 16t t -8 0 = -8(2t 2 - 4t – 1) Use the quadratic formula to find t. a = 2, b = -4, c = -1

( )( ) Set the factors equal to zero and solve. before You must keep the greatest monomial factor that is pulled out before using the X figure! Can you factor out a greatest monomial factor? More factoring and solving. Solve.

8-5 Factoring Differences of Squares Algebra 1 Glencoe McGraw-HillLinda Stamper

Difference of Two Squares factors product Recognizing a difference of two squares may help you to factor - notice the sum and difference pattern. No middle term – check if first and last terms are squares. Sign is negative. Check using FOIL!

Factor. Sign must be negative! prime

Example 1 Check using FOIL! Factor. Example 2 Example 3 Example 4 Example 5 Example 6

Remember to factor completely. Write problem. No middle term – check if first and last terms are squares. Factor – must use parentheses. Check using FOIL! Factor out the GMF.

Sometimes you may need to apply several different factoring techniques. Group terms with common factors. Factor each grouping. Factor the common binomial factor. Check – Multiply the factors together using FOIL. The problem. Factor out the GMF. Factor the difference of squares.

Example 7 Factor. Example 8 Example 9 Example 10

Use factoring to solve the equation. Remember to set each factor equal to zero and then solve! Example 11 Example 12 Example 13 Example 14

Use factoring to solve the equation. Remember to set each factor equal to zero and then solve! Example 11 Example 12

Use factoring to solve the equation. Remember to set each factor equal to zero and then solve! Example 13

Use factoring to solve the equation. Remember to set each factor equal to zero and then solve! Example 14

8-A11 Pages 451 # 11–30.