help!!!

Question

A shotput follows a parabolic path when thrown. athe height (h) of the shotput can be represented by the quadratic function h(d) = -0.022d^2 + d + 5.3 where the height is in feet and 'd' is the horizontal distance the shotput has travelled in feet. Draw an accurate graph for this situation and make sure you label the axis. then answer:

a) what is the value of the h-intercept? what does this represent and why isn't it 0?

b) what is the maximum height of the shotput?

c)what is the value of the d-intercept? what does this represent?

Answer 1

The quadratic function h(d) = - 0. 022d² + d + 5.3

Compare it to parabolic function  f(x) = ax² + bx + c

f(x) = h(d) , x = d

a = -0.022, b = 1, c = 5.3

Find the vertex of h(d) = - 0. 022d² + d + 5.3.

Axis of symmetry x = -b/2a

d = -1/2(-0.022)

d = 1/(0.044)

d = 22.72

Substitute d = 22.72 in  h(d) = - 0. 022d² + d + 5.3

h(22.72) = - 0.022(516.1984) + 22.72 + 5.3

= - 11.35 + 22.72 + 5.3

= 16.67

Vertex = (22.67, 16.67)

Graph

a) From the graph h intercept is  5.3.

It is not zero because h intercept is found by substitute d = 0 in h(d) = - 0. 022d² + d + 5.3.

h(0) = - 0. 022(0)² + 0 + 5.3

h intercept is  5.3.

 

b) Maximum height of shot put = 16.67ft

 

c) From the graph d intercept is 50.22

 d intercepts are found by substitute h(d) = 0 in h(d) = - 0. 022d² + d + 5.3.

 - 0. 022d² + d + 5.3 = 0

Solve the equation by using quadratic formula.

Roots are

Consider the positive value

d intercept is 50.22.