Question

a baseball team manager is trying to determine how the angle at which a ball leaves a players bat impacts the distance the ball travels. the table shows the average distance a baseball travels based on the launch angle of the ball.
launch angle in degrees (x) | 10 | 20 | 30 | 40 | 50
distance in feet (y) | 172 | 303 | 338 | 302 | 245
the quadratic function $y = -0.32x^2 + 20.61x + 5$ models this data.
use the function to estimate the distance a baseball would travel if it were hit at a $55^circ$ angle.
round your answer to the nearest whole number.
\boxed{} feet

Explanation:

Step1: Identify the function and the value of x

We are given the quadratic function \( y = -0.32x^{2}+20.61x + 5 \) and we need to find the value of \( y \) when \( x = 55 \) (since the launch angle is \( 55^\circ \)).

Step2: Substitute x = 55 into the function

Substitute \( x = 55 \) into the function \( y=-0.32x^{2}+20.61x + 5 \):
First, calculate \( x^{2} \) when \( x = 55 \): \( 55^{2}=55\times55 = 3025 \)
Then, calculate \( - 0.32x^{2}\): \( -0.32\times3025=-968 \)
Next, calculate \( 20.61x \): \( 20.61\times55 = 20.61\times(50 + 5)=20.61\times50+20.61\times5 = 1030.5+103.05 = 1133.55 \)
Now, substitute these values back into the function:
\( y=-968+1133.55 + 5 \)

Step3: Calculate the value of y

First, add \( - 968\) and \( 1133.55 \): \( -968+1133.55 = 165.55 \)
Then, add 5 to the result: \( 165.55+5=170.55 \)
Round \( 170.55 \) to the nearest whole number, which is \( 171 \).

Answer:

171