1. For example:
f(x)=6x2+17x-14

3. f(x)=0
f(2)=0 (2,0)
f(5)=0 (5,0)

5. y= 6x 2 +17x-14
Factoring ax 2 +bx+c

6. x= 6 5

7. Zeros are x= 6 5 0=5 x 2 +4x-12 f( 6 5 )=5( 6 5 )2+4( 6 5 )-12
=5( )
f( 6 5 )=12-12=0
We can check by substitution:

8. x= x=-2

9. !

10. Rewrite f(x)= 8x 2 +18x+9 by factoring.
What are the zeros of the quadratic function?

11. Sports. If you throw a softball into the air with an initial upward velocity of 38 ft./s. and an initial height of 5 ft.
Use the vertical motion model
h=-16t2+v0t+h0 to write an equation that give the ball’s height in feet at the time t in seconds.

12. b. The ball’s height is 0 ft. when it is on the ground
b. The ball’s height is 0 ft. when it is on the ground. Solve the equation you wrote in part (a) for h=0 to find when the ball lands.
c. How would graphing the quadratic equation help you understand the problem?

13. Error Analysis. Your friend attempted to solve the equation below
Error Analysis. Your friend attempted to solve the equation below. Can you identify where your friend made a mistake? Now show the correct factorization and solutions of the equation.
y=2x2-7x-4
y=2x(x+4)-(x+4)
0=(2x-1)(x+4) x= and x=-4

14. Error Analysis (continued)
Error Analysis (continued). What method would you choose to convince your friend that x= 1 2 and x=-4 are not the zeros of the function?