Question

A basketball player shoots a ball towards the hoop.

The trajectory of the ball can be modeled by the quadratic functionf(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.



(1 point)
Part A: Identify the vertex (write your answer as an ordered pair):

Part B: Complete the table

x f(x)
0
1
2
3

Answer 1

To analyze the quadratic function \( f(x) = -(x - 1.4)^2 + 6 \), let's address each part of your question.

### Part A: Identify the vertex
The function is in vertex form, \( f(x) = a(x - h)^2 + k \), where \( (h, k) \) is the vertex. Here, \( a = -1 \), \( h = 1.4 \), and \( k = 6 \).

**Vertex:** \( (1.4, 6) \)

### Part B: Complete the table
Next, we will evaluate \( f(x) \) for each given value of \( x \).

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

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

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

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

Now we can summarize the results in the table:

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

### Summary of Answers:
- **Part A (Vertex):** \( (1.4, 6) \)
- **Part B:**
\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
0 & 4.04 \\
1 & 5.84 \\
2 & 5.64 \\
3 & 3.44 \\
\hline
\end{array}
\]