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Dovator [93]
1 year ago
6

1. Quadratics.

Mathematics
1 answer:
Drupady [299]1 year ago
8 0

h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8. This can be obtained by understanding the concepts of graph function.

<h3>What is the value of h(24)?</h3>

Given,

h(x) = -0.017x² + 1.08x + 5.8

Put h = 24,

h(24) = -0.017(24)² + 1.08(24) + 5.8

h(24) = -9.792 + 25.92 + 5.8

h(24) = 21.93

The height of the shot put above the ground is 21.93 feet when the shot is 24 feet horizontally from the start.

<h3>What is the value of the vertical intercept?</h3>

Vertical intercept, x = 0

h(0) = -0.017(0)² + 1.08(0) + 5.8

h(0) = 5.8

The height of the shot put above the ground is 5.8 feet at the start.

<h3>What is the values of the vertex coordinates?</h3>

vertex coordinates,

(h,k) = [(-b/2a),-(b²- 4ac)/4a]

(h,k) = [(-1.08/2(-0.017)),-((1.08)²- 4(-0.017)(5.8))/4(-0.017)]

(h,k) = [(1.08/0.034),(1.5608)/0.068)]

(h,k) = (31.76,22.95)

The maximum height attained by the shot is 22.95 feet when it is horizontally 31.76 feet away from the start.

<h3>How far from the start did the shot put strike the ground?</h3>

Put h(x) = 0,

-0.017x² + 1.08x + 5.8 = 0

Use quadratic formula for solving x,

x = (-b±√b²- 4ac)/2a

Here a = -0.017, b=1.08, c=5.8

x = [-1.08±√1.08²- 4(-0.017)(5.8)]/(2×-0.017)

x = [-1.08±√1.5608]/-0.034

x =  [-1.08-1.2493]/-0.034 and x =  [-1.08+1.2493]/-0.034

x = 68.509 and x = - 4.98

Distance between (68.509,0) and (- 4.98,0) = √[68.509 -(- 4.98)]² + (0-0)²

                                                                        = √73.49²

                                                                        = 73.49 feet              

Hence h(24) = 21.93, vertical intercept is 5.8, (31.76,22.95) are the vertex coordinates and the distance traveled by the shot is 73.49 feet given the equation of the path of the longest shot h(x) = -0.017x² + 1.08x + 5.8.

Learn more about graph:

brainly.com/question/14180189

#SPJ1

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