Question

a ball is thrown upward and outward from a height of 5 feet. the table shows four measurements indicating the balls height at various horizontal distances from where it was thrown. a graphing - calculator displays a quadratic function that models the balls height, y, in feet, in terms of its horizontal distance, x, in feet. answer parts (a)-(c) below.

x, balls horizontal distance (feet)	y, balls height (feet)
1	7.7
3	5
4	3.1

| chartkey |
| ---- |
| y = ax²+bx + c |
| a=-0.8 |
| b = 2.4 |
| c = 5.4 |

1. the height decreases then increases, which looks like a quadratic function.
2. the height decreases quickly at first but then decreases more slowly, which looks like a quadratic function.
3. the height starts decreasing more and more rapidly, which looks like a quadratic function.

in the quadratic regression screen shown in the problem statement, why is the value of the coefficient a negative?

1. since the height increases then decreases, the quadratic graph must open upward, not downward, which means a must be negative.
2. since the height increases then decreases, the quadratic graph must open downward, not upward, which means a must be negative.
3. since the height of the ball starts at the height of the person throwing the ball, the quadratic graph must be shifted up, which makes a negative.
4. use the graphing - calculator screen (shown in the box above) to express the model in function notation.

f(x)=

Explanation:

Step1: Recall quadratic function form

The quadratic function is $y = ax^{2}+bx + c$, and we are given $a=-0.8$, $b = 2.4$, $c = 5.4$.

Step2: Write function notation

The function notation for the height of the ball in terms of horizontal distance $x$ is $f(x)=-0.8x^{2}+2.4x + 5.4$.

Answer:

$f(x)=-0.8x^{2}+2.4x + 5.4$