Problem
Christopher Malone $06 / 12 / 2310: 16 \mathrm{PM}$ Score: $12.24 \%, 0.86$ of 7 points Points: 0 of 1 (a) An athlate whose event is the shot put releases a shot. When the shot whose path is shown by the graph to the right is released at an cond $f(x)=-0.01 x^{2}+0.7 x+5.9$ where $x$ is the shot's horizontal distance, in feet, from its point of release. Use this model to solve parts (a) through (c) and verify your answers using the graph a. What is the maximum height of the shot and how far from its point of release does this occur? The maximum height is $\square$, which occurs $\square$ feet from the point of release. Type an integer or decimal rounded to four decimal places as needed.) Help me solve this View an example Get more help. Clear all
Solution
Step 1 ：Given the function \(f(x) = -0.01x^2 + 0.7x + 5.9\), we need to find the vertex to determine the maximum height of the shot.
Step 2 ：Using the formula \(x = -\frac{b}{2a}\), where \(a = -0.01\) and \(b = 0.7\), we can find the x-coordinate of the vertex.
Step 3 ：\(x = -\frac{0.7}{2(-0.01)} = 35\)
Step 4 ：Plug the x-coordinate back into the function to find the maximum height: \(f(35) = -0.01(35)^2 + 0.7(35) + 5.9\)
Step 5 ：\(f(35) = 18.15\)
Step 6 ：\(\boxed{\text{The maximum height of the shot is 18.15 feet, which occurs 35 feet from the point of release.}}\)
