8.2.2 Zero Product Property Supplement
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Zero Product Property When the product of 2 or more numbers is zero, one of the numbers must be zero. We can use this
property to find the solutions to a quadratic equation that can be factored.
•The solutions to a quadratic equation are known as the zeros or roots.
• If a quadratic equation can by factored, the zeros or roots are the x-coordinate of the x-intercept(s).
Solve by factoring:
𝑓 𝑥 = 2𝑥 ! + 5𝑥 − 12
Find the roots: 𝑓 𝑥 = 2𝑥 ! − 8𝑥 − 90:
Making Connections
1.
𝑦 = 𝑥 ! + 5𝑥 + 6
X
Y
Find the vertex:
Is there symmetry?
Where?
Is it a maximum or a minimum?
Where?
Find the y-intercept (as an ordered pair):
Find the roots (as an ordered pair):
Algebraically
-3
-2
-1
0
1
2
3
X
Y
2. 𝑦 = 𝑥 ! − 𝑥 − 20
-4
-3
-2
-1
0
1
2
3
4
Find the vertex:
Is there symmetry?
Where?
Is it a maximum or a minimum?
Where?
Find the y-intercept (as an ordered pair):
Find the roots (as an ordered pair):
Algebraically
Solve using Zero Product Property. Use the calculator to double check. (Show work on notebook paper)
3. 𝑦 = 6𝑥 ! − 11𝑥 + 4
4. 𝑦 = 5𝑥 ! + 6𝑥 + 1
5. 𝑦 = 3𝑥 ! + 5𝑥 − 2
6. 𝑦 = 4𝑥 ! − 3𝑥 − 1
7. 𝑦 = 𝑥 ! − 64
8. 𝑦 = 𝑥 ! − 12𝑥 + 36
9. 𝑦 = 16𝑥 ! − 9
10. 𝑦 = 3𝑥 ! + 15𝑥 + 18
11. 𝑦 = 5𝑥 ! − 35𝑥 + 60
12. 𝑦 = 2𝑥 ! + 16𝑥 + 24
13. 𝑥 ! − 12𝑥 = −11
14. 6𝑥 ! + 15 = 19𝑥
5