A basketball player shoots a ball towards the hoop.

Question

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:

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