Question

a ball is thrown upward and outward from a height of 7 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)

x, balls horizontal distance (feet)	y, balls height (feet)
1	7.6
3	7
4	2.5

quadreg
$y = ax^{2}+bx + c$
$a=-0.9$
$b = 2.4$
$c = 6.7$

in the quadratic regression screen shown in the problem statement, why is the value of the coefficient a negative?
a. since the height increases then decreases, the quadratic graph must open downward, not upward, which means a must be negative.
b. since the height increases then decreases, the quadratic graph must open upward, not downward, which means a must be negative.
c. 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.

Explanation:

The height of the ball first increases and then decreases as the horizontal distance increases. For a quadratic function \(y = ax^{2}+bx + c\), when \(a<0\), the parabola opens downward which models a quantity that first goes up and then comes down. When \(a > 0\), the parabola opens upward.

Answer:

A. Since the height increases then decreases, the quadratic graph must open downward, not upward, which means a must be negative.