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

Answer:A) h(2.4) is 2.53B) The numerical value of the vertical intercept is 5.8C) The numerical value of the vertex is [tex](\frac{60}{113},\frac{3439}{565})[/tex]D) The shot put strike the ground at x = 2.98Step-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 groundA)- 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 2.53B)- 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 5.8C)- 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