The path of the longest shot put is modeled by h(x)=-1.017x^2+1.08x+5.8, x is the horizontal distance from start and h(x) is the height of the shot put above the ground. a) determine h(24), round to 2 decimal places. b) determine numerical value of the vertical intercept. c) determine numerical value of the vertex. d)how far from start did the shot put strike the ground

A) h(2.4) is 2.53

B) The numerical value of the vertical intercept is 5.8

C) The numerical value of the vertex is

D) The shot put strike the ground at x = 2.98

Step-by-step explanation:

* Lets explain how to solve the problem

- The path of the longest shot put is modeled by

  h(x)= -1.017x² + 1.08x + 5.8, where x is the horizontal distance from

  start and h(x) is the height of the shot put above the ground

A)

- We need to find h(2.4), that means substitute x in the equation by 2.4

∵ h(x)= -1.017x² + 1.08x + 5.8

∵ x = 2.4

∴ h(2.4)= -1.017(2.4)² + 1.08(2.4) + 5.8 = 2.53

∴ h(2.4) = 2.53

* h(2.4) is 2.53

B)

- We need to find the numerical value of the vertical intercept

- That means the y-intercept of the graph of the path ⇒ h(0)

- To find the vertical intercept put x = 0 in the equation

∴ h(0) = 0 + 0 + 5.8

* The numerical value of the vertical intercept is 5.8

C)

- We need to find the numerical value of the vertex

∵ h(x)= -1.017x² + 1.08x + 5.8 is a quadratic function

∴ The coordinates of its vertex are (v , w), where v

   and w = h(v), a is the coefficient of x² and b is the coefficient of x

∵ a = -1.017 and b = 1.08

∴ v =

∵ w = f(v)

∴ w =

* The numerical value of the vertex is

D)

- We need to find how far from start the shot put strike the ground

- That means h(x) = 0, because the height at the ground = 0

∴ -1.017x² + 1.08x + 5.8 = 0

- Use your calculator to find the value of x

∴ x = 2.977 and x = -1.915

- We will ignore the negative value of x because we need the final

 put strike on the ground from the start

∴ x = 2.98

* The shot put strike the ground at x = 2.98