Translate Sentences into Equations x px q 0

Translate Sentences into Equations (x – p)(x – q) = 0 Write the pattern. Replace p with and q with – 5. Simplify. Use FOIL.

Translate Sentences into Equations Multiply each side by 2 so b and c are integers. Answer:

A. ans B. ans C. ans D. ans

Factor GCF A. Solve 9 y 2 + 3 y = 0 3 y(3 y) + 3 y(1) = 0 3 y(3 y + 1) = 0 3 y + 1 = 0 y=0 Answer: Original equation Factor the GCF. Distributive Property Zero Product Property Solve each equation.

Factor GCF B. Solve 5 a 2 – 20 a = 0 5 a(a) – 5 a(4) = 0 5 a(a – 4) = 0 5 a = 0 a– 4=0 a=4 Answer: 0, 4 Original equation Factor the GCF. Distributive Property Zero Product Property Solve each equation.

Solve 12 x – 4 x 2 = 0. A. 3, 12 B. 3, – 4 C. – 3, 0 D. 3, 0

Perfect Squares and Differences of Squares A. Solve x 2 – 6 x + 9 = 0. x 2 = (x)2; 9 = (3)2 First and last terms are perfect squares. 6 x = 2(x)(3) Middle term equals 2 ab. x 2 – 6 x + 9 is a perfect square trinomial. x 2 + 6 x + 9 = 0 (x – 3)2 = 0 x– 3 =0 x =3 Answer: 3 Original equation Factor using the pattern. Take the square root of each side. Add 3 to each side.

Perfect Squares and Differences of Squares B. Solve y 2 = 36 y 2 – 36 = 0 Original equation Subtract 36 from each side. y 2 – (6)2 = 0 Write in the form a 2 – b 2. (y + 6)(y – 6) = 0 Factor the difference of squares. y+6=0 Zero Product Property y– 6=0 y = – 6 Answer: – 6, 6 y=6 Solve each equation.

Solve x 2 – 16 x + 64 = 0. A. 8, – 8 B. 8, 0 C. 8 D. – 8

Factor Trinomials A. Solve x 2 – 2 x – 15 = 0. ac = – 15 a = 1, c = – 15

Factor Trinomials x 2 – 2 x – 15 = 0 Original equation x 2 + mx + px – 15 = 0 Write the pattern. x 2 + 3 x – 5 x – 15= 0 m = 3 and p = – 5 (x 2 + 3 x) – (5 x + 15) = 0 x(x + 3) – 5(x + 3) = 0 (x – 5)(x + 3) = 0 x– 5=0 x+3 =0 x=5 Answer: 5, – 3 x = – 3 Group terms with common factors. Factor the GCF from each grouping. Distributive Property Zero Product Property Solve each equation.

Factor Trinomials B. Solve 5 x 2 + 34 x + 24 = 0. ac = 120 a = 5, c = 24

Factor Trinomials 5 x 2 + 34 x + 24 = 0 Original equation 5 x 2 + mx + px + 24 = 0 Write the pattern. 5 x 2 + 4 x + 30 x + 24= 0 m = 4 and p = 30 (5 x 2 + 4 x) + (30 x + 24) = 0 Group terms with common factors. x(5 x + 4) + 6(5 x + 4) = 0 Factor the GCF from each grouping. (x + 6)(5 x + 4) = 0 x+6=0 x = – 6 5 x + 4 = 0 Distributive Property Zero Product Property Solve each equation.

Factor Trinomials Answer:

Solve 6 x 2 – 5 x – 4 = 0. A. B. C. D.

B. Factor 3 s 2 – 11 s – 4. A. (3 s + 1)(s – 4) B. (s + 1)(3 s – 4) C. (3 s + 4)(s – 1) D. (s – 1)(3 s + 4)

Solve Equations by Factoring ARCHITECTURE The entrance to an office building is an arch in the shape of a parabola whose vertex is the height of the arch. The height of the arch is given by h = 9 – x 2, where x is the horizontal distance from the center of the arch. Both h and x are measured in feet. How wide is the arch at ground level? To find the width of the arch at ground level, find the distance between the two zeros.

Solve Equations by Factoring 9 – x 2 = 0 Original expression x 2 – 9 = 0 Multiply both sides by – 1. (x + 3)(x – 3) = 0 x + 3 = 0 or x – 3 = 0 x = – 3 x= 3 Difference of squares Zero Product Property Solve. Answer: The distance between 3 and – 3 is 3 – (– 3) or 6 feet.

Solve Equations by Factoring Check 9 – x 2 = 0 2 ? 9 – (3) = 0 ? 9– 9= 0 0= 0 or 2 ? 9 – (– 3) = 0 ? 9– 9 =0 0 =0

TENNIS During a match, Andre hit a lob right off the court with the ball traveling in the shape of a parabola whose vertex was the height of the shot. The height of the shot is given by h = 49 – x 2, where x is the horizontal distance from the center of the shot. Both h and x are measured in feet. How far was the lob hit? A. 7 feet B. 11 feet C. 14 feet D. 25 feet

• Section 3 (pg 242): • 17 – 67 odd, 66 (27 problems)