Answer:
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 [tex](\frac{60}{113},\frac{3439}{565})[/tex]
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 [tex]\frac{-b}{2a}[/tex]
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 = [tex]\frac{-1.08}{2(-1.017)}=\frac{60}{113}[/tex]
∵ w = f(v)
∴ w = [tex]-1.017(\frac{60}{113})^{2}+1.08(\frac{60}{113}) + 5.8=\frac{3439}{565}[/tex]
* The numerical value of the vertex is [tex](\frac{60}{113},\frac{3439}{565})[/tex]
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
