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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 Skip to navigation

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To analyze the quadratic function \( f(x) = -(x + 1.4)^2 + 6 \), we can break down the two parts you've mentioned.

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 of the parabola. In this case, the function is given as:

\[ f(x) = -(x + 1.4)^2 + 6 \]

We can rewrite this in vertex form:

  1. The vertex is found directly from the expression \( -(x + 1.4)^2 + 6 \).
  2. Here, \( h = -1.4 \) and \( k = 6 \).

Thus, the vertex is:

\[ \text{Vertex} = (-1.4, 6) \]

Part B: Complete the table

Now we'll calculate \( f(x) \) for the given values \( x = 0, 1, 2, \) and \( 3 \).

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

  2. \( x = 1 \): \[ f(1) = -((1) + 1.4)^2 + 6 = -(2.4)^2 + 6 = -5.76 + 6 = 0.24 \]

  3. \( x = 2 \): \[ f(2) = -((2) + 1.4)^2 + 6 = -(3.4)^2 + 6 = -11.56 + 6 = -5.56 \]

  4. \( x = 3 \): \[ f(3) = -((3) + 1.4)^2 + 6 = -(4.4)^2 + 6 = -19.36 + 6 = -13.36 \]

Now, we can summarize these results in the table:

| x | f(x) | |-----|----------| | 0 | 4.04 | | 1 | 0.24 | | 2 | -5.56 | | 3 | -13.36 |

Summary of Answers:

  • Part A: Vertex = \( (-1.4, 6) \)
  • Part B:

| x | f(x) | |-----|----------| | 0 | 4.04 | | 1 | 0.24 | | 2 | -5.56 | | 3 | -13.36 |