Start-Up - Quadratic Functions
1. Graph the function f(x)=x2+10x+16
a. What is the equation for the line of symmetry?
b. What is the vertex?
c. What are the solutions?
2. Write a quadratic equation with 8 and -4 as the solutions.
3. Find the solutions by factoring to the function f(x)=x2-7x+12
4. If 7 is a root of the equation y  2x 2  kx  7 , what is k?
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5. What are the roots of the graph below?
Objective: Students will be able to solve a quadratic equation by factoring.
A QUADRATIC EQUATION is in the form:
When we factor, we look to find two number that…
Key Question: What happens if a  1 or  1 ?
1. How can we factor 2x 2  6x  4  0 ?
We can factor this quadratic by first finding the GCF (___________________)!
In this example the GCF=________.
2. How can we factor x 2  6x  0 ?
In this example the GCF=_________.
3. How can we factor 5 x 2  15x  0
In this example the GCF=_________.
Factor each equation to find the solutions.
1. 3x2 - 3x = 0
6. 4x2-4x = 0
2. 33x2 + 363x = 0
7. 10x2-20x+10 = 0
3. -33x2 - 330x = 0
8. x2-14x = 0
4. 12x2 – 5x = 0
9. x3+7x2+12x = 0
5. 3x3+18x2+24x = 0
10. 4x2 – 48x = 0
Mixed practice: Solve for x in each equation.
11. x2+100=-20x
19. 4x2-36x=0
12. 2x2 – 16x – 18 = 0
13.
5x2+3x+2=0
14.
x2
20. x2 = 11x
21. (x-5)(x+6)=0
– 8x=20
22. x2 + 48 = 16x
15. 6x2 + 66x + 180=0
23. -11x2 + 66x = 88
16. x2-7x=0
17.
-3x2
18.
x2
24. x2 - 7x + 6 = 0
– 15x + 150=0
+ x = 90
25. x2 – 100 = 0
When I have a quadratic expression, the first thing I look to do is
____________________________!