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


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Answer 1

the table says misplaced /hline

Answer 2

To analyze the quadratic function \( f(x) = -(x - 1.4)^2 + 6 \), let's start with Part A and find the vertex of the function.

### Part A: Identify the Vertex
The vertex form of a quadratic function is given by \( f(x) = a(x - h)^2 + k \), where \( (h, k) \) is the vertex.

In the given function:
- \( h = 1.4 \)
- \( k = 6 \)

Thus, the vertex is:
**Vertex: \( (1.4, 6) \)**

### Part B: Complete the Table
Next, we will calculate the values of \( f(x) \) for given values of \( x \) (0, 1, 2, and 3).

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

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 fill in the table:

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

### Final answers:

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

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