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) below.

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

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.
b. use the graphing calculator screen (shown in the box above) to express the model in function notation.
f(x)=

Explanation:

Step1: Recall the quadratic - function form

The general form of a quadratic function is $y = ax^{2}+bx + c$. In function - notation, we replace $y$ with $f(x)$.

Step2: Substitute the given values of a, b, and c

We are given that $a=-0.9$, $b = 2.4$, and $c = 6.7$.
So, $f(x)=-0.9x^{2}+2.4x + 6.7$.

Answer:

$f(x)=-0.9x^{2}+2.4x + 6.7$