Question

julie and Annie each throw a softball into the air. The function f, where f(x)=3+18x−5x2, gives the height of Julie's softball, in meters, x seconds after throwing the ball.The graph represents the height of Annie's softball, in meters, x seconds after throwing the softball..

Answer 1

The softball was thrown higher by Julie. Her softball reached a maximum height of 19.2 meters, 1.8 seconds after throwing the softball.

By critically observing the graph shown above, we can logically deduce the following information about Annie's softball;

Maximum height (peak y-value) = 14.4 meters.

Time to reach maximum height = 1.5 seconds.

In order to determine the maximum height of Julie's softball, we would have to calculate the time it took her softball to reach the maximum height by using the axis of symmetry formula;

x = -b/2a

x = -18/2(-5)

x = 18/10

x = 1.8 seconds.

Now, we can determine the maximum height of Julie's softball;

`f(x)=3+18x-5x^2\\\\f(1.8)=3+18x-5(1.8)^2`

f(1.8) = 19.2 meters.

Complete Question:

Julie and Annie each throw a softball into the air. The function ƒ, where
`f(x)=3+18x-5x^2`, gives the height of Julie's softball, in meters, x seconds after throwing the ball. The graph represents the height of Annie's softball, in meters, x seconds after throwing the softball.

Select from the drop-down lists to complete each sentence correctly.

The softball was thrown higher by ___. Her softball reached a maximum height of ___ meters, ___ seconds after throwing the softball.

Answer 2

Given,

The function for the height of the ball is f(x) = 3+18x−5x^2.

Required

The maximum height of the ball.

The maximum height of the ball is obtained by derivative of the height function and equate it to 0.

Differentiating the function with respect to x,

`\begin{gathered} f(x)=3+18x-5x^2 \\ f^(\prime)(x)=(d)/(dx)(3+18x-5x^2) \\ f^(\prime)(x)=0+18-10x \\ f^(\prime)(x)=18-10x \end{gathered}`

Taking f'(x) =0 then,