Question

a tennis player hits a lob shot. the height of the ball can be modeled by the quadratic function $f(x) = -\frac{1}{2}x^2 + 5x$, where $f(x)$ represents the height of the ball in feet after $x$ seconds. which statement represents the height of the ball after 3 seconds? a. $f(3) = 19\frac{1}{2}$ b. $f(19\frac{1}{2}) = 3$ c. $f(3) = 10\frac{1}{2}$ d. $f(10\frac{1}{2}) = 3$

Explanation:

Step1: Substitute \( x = 3 \) into the function

We have the function \( f(x)=-\frac{1}{2}x^{2}+5x \). To find the height after 3 seconds, we substitute \( x = 3 \) into the function. So we calculate \( f(3)=-\frac{1}{2}(3)^{2}+5(3) \).

Step2: Calculate each term

First, calculate \( (3)^{2}=9 \), then \( -\frac{1}{2}\times9 = -\frac{9}{2}=-4.5 \). Next, calculate \( 5\times3 = 15 \).

Step3: Sum the terms

Now, add the two results together: \( -4.5 + 15 = 10.5=10\frac{1}{2} \). So \( f(3)=10\frac{1}{2} \).

Answer:

C. \( f(3) = 10\frac{1}{2} \)