Question

ANY HELP WOULD BE REALLY APPRECIATED

Suppose Brett and Andre each throw a baseball into the air. The height of Brett's baseball is given by h(t) = −16t^2 + 79t + 6, where h is in feet and t is in seconds. The height of Andre's baseball is given by the graph below (it's the attached image). Brett claims that his baseball went higher than Andre's, and Andre says that his baseball went higher.
1. Who is right? Fill out the table below to justify your answer. Approximate
when necessary (table is second attached image).

Answer 1

One could make a graph for Bret's baseball, just like Andre's graph, plotting height at each half second of time using the given equation. Then compare the heights at every half second for the two graphs using the Brett vs Andre chart.

Answer 2

1. Brett was right because her baseball reached a maximum height of 103.52 feet.

2. A table that justifies Brett's claim is shown below.

In Mathematics and Geometry, the maximum value of any function is a point on the graph where the function reaches its highest point. Additionally, the maximum value of Brett's quadratic function can be determined by finding the axis of symmetry;

Axis of symmetry, x = -b/2a

`h(t) = -16t^2 + 79t + 6`

where:

a = -16, b = 79, and c = 6.

By substituting the values of a and b into the formula, we have;

Axis of symmetry, x = -79/2(-16)

Axis of symmetry, x = 79/32 = 2.46875.

Now, we can determine the maximum value (vertex) as follows;

`h(t) = -16t^2 + 79t + 6\\\\h(2.46875) = -16(2.46875)^2 + 79(2.46875) + 6`

h(2.46875) = 103.52 feet.

Based on the graph, we can logically deduce that the maximum height attained by Andre's baseball was below 80 feet. Hence, Brett was right.

Lastly, we would complete the table as follows;

t Brett Andre

0 6 6

1 69 58

2 100 78

3 99 67

4 66 6

5 0

In conlusion, we can logically deduce that Brett was right because her baseball reach a maximum height of 103.52 feet, which was greater than Andre's.