# Thread: Quadratic Graphing Problem, Need Help

1. ## Quadratic Graphing Problem, Need Help

Hi, I need someone to help guide me through the following problem:

A football player kicks a ball at an angle of 37° above the ground with an initial speed of 20 meters per second. The height, h, as a function of the horizontal distance traveled, d, is given by: $\displaystyle h(d) = 0.75 - 0.00192d^2$

A. Graph the path of the ball as follows
B. When the ball hists the ground, how far is it from the spot where the football player kicked it?
C. What is the maximum height the ball reaches during its flight?
D. What is the horizontal distance the ball has traveled when it reaches its maximum height?

2. A. To graph the equation using pen and paper, plot points and then join them up. Eg. if x = 1, then y = 0.75192. If x = 2, y = 0.75384. And so on...

B. Use the quadratic formula: $\displaystyle d = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ You will get 2 answers, use the one most appropriate for the distance travelled.

C. Differentiate the equation, then substitute in h'(d) = 0. (Gradient 0) This will give you the distance. Substitute this value into your original equation to find the maximum height.

D. The horizontal distance travelled is the area under the graph, so you have to integrate it. Can you figure it out for yourself?