Question

Home Run Derby

Data are shown below for three baseball players at a recent minor league home run hitting contest.

Juan:
The ball followed a path modelled by the equation h = −0.001! + 0.5 + 2.5 where h is the height of the ball in feet and is the horizontal distance in feet.



1) Represent the distance-height relationship for each player’s ball as an equation, in a table and on a graph. Record each representation and clearly label which player the information belongs to.



2) Supposed there were no obstacles.



a. Whose ball would travel the greatest distance before hitting the ground?



b. Whose ball would travel the shortest distance before hitting the ground?

3) Suppose the fence was 350 ft from home plate. At what height was each ball when it passed over the fence?

Answer 1

Juan's ball would travel the greatest distance while Barry's ball would travel the shortest.

Represent the distance-height relationship for each player’s ball as an equation, in a table and on a graph.

Juan

Juan's equation is given as:

h = -0.001d^2 + 0.5d + 2.5

h =

Set d to multiples of 50 from 0 to 400.

So, the table of values of Juan's function is:

d (ft)                   h(ft)

0                          2.5

50                        25

100                      42.5

150                        55

200                      62.5

250                        65

300                      62.5

350                        65

400                      42.5

See attachment for the graph of Juan's function

Mark

A quadratic function is represented as:

h = ad^2 + bd + c

Using the values on the table of values, we have:

c = 3 -- the constant value

So, the equation becomes

h = ad^2 + bd + 3

Using the two other values on the table of values, we have:

23 = a(50)^2 + b(50) + 3

38 = a(100)^2 + b(100) + 3

Using a graphing tool, we have:

a = -0.001

b = 0.45

So, Mark's equation is h(d) = -0.001d^2 + 0.45d + 3

See attachment for Mark's graph.

Barry

From the graph, we have the table of values of Barry's function to be:

d (ft)                   h(ft)

0                          2.5

50                        21

100                      35

150                       44

200                      48

250                       46

300                      41

350                       30

400                      14

450                      0

Using a graphing tool, we have the quadratic function to be:

y = -0.001x^2 +0.4x +2.5

The shortest and the greatest distance before hitting the ground

From the graphs, equations and tables, the distance travelled by the balls are:

Juan = 505 feet

Mark = 457 feet

Barry = 450 feet

This means that Juan's ball would travel the greatest distance while Barry's ball would travel the shortest.

The height the balls hit a fence at 350 ft distance

To do this, we set d = 350

From the graphs, equations and tables, the height at 350 ft by the balls are:

Juan = 65 feet

Mark = 38 feet

Barry = 30 feet

The above represents the height the balls hit the fence

Read more about quadratic functions at:

https://brainly.com/question/12446886

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