a The maximum height of the ball is the y-coordinate of the vertex of the given function.
B
b The ball will clear the net if at x=30 the height y is greater than 3 ft.
A
aMaximum height: 4.445 ft
B
b The ball will clear the net. See solution.
Practice makes perfect
a Let's analyze the given function.
y=- 0.005x^2+0.17x+3
The variable y represents the height in feet of a tennis ball x feet from where you hit the ball. We are asked to find the maximum height of the ball. The given function is in the form of y= ax^2+bx+c. Let's begin by highlighting the coefficients.
f(t)= - 0.005t^2+0.17t+3
Since the coefficient a is negative, the given quadratic function opens downward. Therefore, its maximum value will be at the vertex. First we will find the x-coordinate of the vertex. It can be found by using the formula x=- b2 a.
b We are standing 30 feet from the net, which is 3 feet high. Therefore, the ball will clear the net if at x=30 the height of the ball is greater than 3 feet. Let's substitute x=30 into the given function and check!
