Quadratic Function Help?

Question

I have a test tomorrow on this unit and I need someone to explain to me how to answer the following question (listing the steps in the simpilest way) would be great:

1. The path of the ball for many golfers shots can be modelled by a quadratic function. The path of a golf ball hit at an angle of about 10 degrees to the horizontal can be moddeled by a function: h= -0.002d^2+0.4d (h=the height of ball in meters, d=the horizontal distance the ball travels in meters util it first hits the ground).

a) What is the maximum height reached by the ball?

b) What is the horizontal distance of the ball from the golfer when the ball reaches its maximum height?

Answer 1

a) Since the graph points down, the max is the vertex. The x-value of te vertex is (-b)/(2a)

So, in this case, -0.4/-0.004

x=100

However, you want to know the height, not the horizontal distance, so solve for y.

y = -0.002(100^2) + 0.4(100)

y = -0.002(10000) + 40

y = -20 + 40

y = 20 meters.

b) okay... well, you already know this from a because you had to find it first... and it's 100 meters. You find that by using

(-b)/(2a) in the equation ax^2 + bx + c