5-5 Quadratic Equations Hubarth Algebra II

For every real number a, b, if ab = 0, then a = 0 or b = 0. Zero Product Property For every real number a, b, if ab = 0, then a = 0 or b = 0. EXAMPLE If (x + 3)(x + 2) = 0, then x + 3 = 0 and x + 2 = 0 Ex 1 Using the Zero Product Property Solve (2x + 3)(x – 4) = 0 by using the Zero-Product Property. 2x + 3 = 0 or x – 4 = 0 x = 4 2x = –3 x = – 3 2

Ex 2 Solving by Factoring Solve 3x2 – 2x = 21 by factoring. 3x2 – 2x – 21 = 0 (3x + 7)(x – 3) = 0 3x + 7 = 0 or x – 3 = 0 3x = –7 x = 3 x = – 7 3

Ex 3 Solve by Finding Square Roots Solve 3x2 – 75 = 0. 3x2 – 75 + 75 = 0 + 75 3x2 = 75 x2 = 25 x = ± 25 x = ± 5

Ex. 4 Real-World Connection Firefighting Smoke jumpers are in free fall from the time they jump out of a plane until they open their parachutes. The function 𝑦=−16 𝑡 2 +1600 models a jumper’s height y in feet at t seconds for a jump from 1600ft. How long is a jumper in free fall if the parachute opens at 1000ft? 𝑦=−16 𝑡 2 +1600 1000=−16 𝑡 2 +1600 −600=−16 𝑡 2 37.5= 𝑡 2 𝑡≈±6.1 The jumper is in free fall for approximately 6.1 seconds

Practice 1. Solve each equation by factoring. a. 2 𝑥 2 +4𝑥=6 b. 16 𝑥 2 =8𝑥 −3, 1 0, 1 2 2. Solve each equation by finding square roots. a. 4 𝑥 2 −25=0 b. 3 𝑥 2 =24 ± 5 2 ±2 2 3. A smoke jumper jumps from 1400ft. The function describing the height is 𝑦=−1600 𝑡 2 +1400. Using square roots, find the time during which the jumper is in free fall if the parachute opens at 1000ft. 5 seconds