1. You have 60 in. of molding to use as a frame around a picture you are painting. The area of the painting is giving by the function y = 30x - x^2 where x is the width in inches. What width gives the maximum area for the painting? What is the maximum area?

2. You are trying to dunk a basketball. You need to jump 2.5 ft in the air in order to dunk the ball. The height that your feet are above the ground is given by the function h = -16t^2 + 12t. What is the maximum height your feet will be above the ground? Will you be able to dunk the basketball?

I need a lot of help with these problems. Please answer them to the best of your capabilities. I'M GOING INSANE!!! Thanks so much!

1) [tex]y = 30x - x^2 y = -x^2+30x (y = ax^2+b)[/tex]

[tex]x = -b/2a = -30/2(-1) = 15[/tex]

[tex]y = -(15)^2+20(15) y = -225+450 y = 225[/tex]

So, 15 as the width would give us the maximum area for the painting.
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2) The maximum height your feet will be above the ground is 2.25 ft.
No, you wouldn't be able to dunk the ball because the maximum height you can jump is 2.25, but you need to jump 2.5 ft to dunk.