1. Completing the Square Quadratic Formula
Sec. 1.4 cont.
Completing the Square
Quadratic Formula

2. Completing the Square
The purpose of completing the square is to develop a perfect square trinomial so you can factor it down to a binomial squared

3. Steps in completing the square
Get the constant on one side by itself and the x2 + bx part on the other.
Add to both sides
Factor the new trinomial
Extract the roots

4. Ex. 3

5. Important
The leading coefficient must be 1 or you have to divide both sides of the equation by the lead coefficient to make it 1 before completing the square.

6. Ex.
3x2 – 4x – 5 = 0

7. Quadratic Formula
For
ax2 + bx + c = 0

8. Located under the radical
Discriminant
b2 – 4ac
Located under the radical

9. The discriminant lets us tell the number of solutions
Positive
Zero
Negative
2 distinct real solutions
1 repeated solution
No real solutions

10. Ex. 4
x2 + 3x = 9

11. Ex. 5
A bedroom is 3 ft. longer than it is wide. The area is 154 sq. ft. Find the dimensions

12. Position Equation
Gives the height of something falling or thrown into the air.

13. s = -16t2 + v0t + s0
s is the height in feet of the object at a given time.
v0 is the initial (original) velocity ft/s
s0 is the original height of the object in ft.
t is the time
The -16 is acceleration due to gravity in ft/s2

14. Ex. 6
A construction worker on the 24th floor drops a wrench and yells. Could a person below hear in time to get out of the way?