1. 5-5 Quadratic Equations
Hubarth
Algebra II

2. 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 = or x – 4 = 0
x = 4
2x = –3
x = – 3 2

3. 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

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

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 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
1000=−16 𝑡
−600=−16 𝑡 2
37.5= 𝑡 2
𝑡≈±6.1
The jumper is in free fall for approximately 6.1 seconds

6. 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 Using square roots, find the time during which the jumper
is in free fall if the parachute opens at 1000ft.
5 seconds