Question

A basketball player shoots a ball towards the hoop.

The trajectory of the ball can be modeled by the quadratic function f(x) = −(x−1.4)2+6
, where x represents the horizontal distance in feet from the player, and f(x) represents the height of the ball in feet
Complete the table

x f(x)
0
1
2
3

Answer 1

To complete the table for the function \( f(x) = -(x - 1.4)^2 + 6 \), we will calculate the value of \( f(x) \) for each value of \( x \) provided.

1. For \( x = 0 \):
\[
f(0) = - (0 - 1.4)^2 + 6
\]
\[
= - (1.96) + 6
\]
\[
= 6 - 1.96 = 4.04
\]

2. For \( x = 1 \):
\[
f(1) = - (1 - 1.4)^2 + 6
\]
\[
= - (-0.4)^2 + 6
\]
\[
= - (0.16) + 6
\]
\[
= 6 - 0.16 = 5.84
\]

3. For \( x = 2 \):
\[
f(2) = - (2 - 1.4)^2 + 6
\]
\[
= - (0.6)^2 + 6
\]
\[
= - (0.36) + 6
\]
\[
= 6 - 0.36 = 5.64
\]

4. For \( x = 3 \):
\[
f(3) = - (3 - 1.4)^2 + 6
\]
\[
= - (1.6)^2 + 6
\]
\[
= - (2.56) + 6
\]
\[
= 6 - 2.56 = 3.44
\]

Now we can summarize the results in the completed table:

\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
0 & 4.04 \\
1 & 5.84 \\
2 & 5.64 \\
3 & 3.44 \\
\hline
\end{array}
\]