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.
(1 point)
Part A: Identify the vertex (write your answer as an ordered pair):
3 answers
To find the vertex of the quadratic function \( f(x) = - (x + 1.4)^2 + 6 \), we note that it is written in vertex form, which is \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex.
In this case, we can identify:
Therefore, the vertex of the function \( f(x) \) is \((-1.4, 6)\).
Answer: \((-1.4, 6)\)
To complete the table, we will substitute the values of \( x \) into the function \( f(x) = - (x + 1.4)^2 + 6 \) and calculate \( f(x) \) for each value.
For \( x = 0 \): \[ f(0) = - (0 + 1.4)^2 + 6 = - (1.4)^2 + 6 = -1.96 + 6 = 4.04 \]
For \( x = 1 \): \[ f(1) = - (1 + 1.4)^2 + 6 = - (2.4)^2 + 6 = -5.76 + 6 = 0.24 \]
For \( x = 2 \): \[ f(2) = - (2 + 1.4)^2 + 6 = - (3.4)^2 + 6 = -11.56 + 6 = -5.56 \]
For \( x = 3 \): \[ f(3) = - (3 + 1.4)^2 + 6 = - (4.4)^2 + 6 = -19.36 + 6 = -13.36 \]
Now, we can fill in the completed table:
| \( x \) | \( f(x) \) | |:-----------:|:--------------:| | 0 | 4.04 | | 1 | 0.24 | | 2 | -5.56 | | 3 | -13.36 |
This is the completed table.
