## anonymous 4 years ago A ball in flight is modeled by the function h(t)=-16t²+128t. Find the maximum height and time to get there.

1. Mertsj

The maximum height will be the y coordinate of the vertex. Can you find that?

2. anonymous

huh?

3. Mertsj

Do you know that the graph of that function is a parabola?

4. anonymous

yes

5. Mertsj

So then you know that it has either a high point or a low point?

6. anonymous

yes

7. Mertsj

which one does this problem have...a high point (maximum) or a low point (minimum)?

8. anonymous

maximum

9. Mertsj

It has a hight point (maximum) because the coefficient of the t^2 term is negative.

10. Mertsj

Do you know that the high point is called the vertex?

11. anonymous

yes

12. Mertsj

Do you know that the vertex is represented by an ordered pair that has an x value and a y value?

13. anonymous

yes

14. Mertsj

Ok. we need to find that highest point (vertex). The x coordinate of the vertex is x=-b/2a Calculate that.

15. Mertsj

$x=\frac{-128}{2(-16)}=\frac{-128}{-32} = 4$

16. Mertsj

$y=-16(4)^2+128(4)= 256$

17. Mertsj

So the vertex is (4,256) and the maximum height of the ball is 256 feet.

18. Mertsj

And that happens when the time is 4 seconds.