Question

Derrick made a goal for 2 points during the basketball game. The path of the balls height in feet can be modeled by y=-x^2 -2x +24.use a graph of the function to determine the maximum height of the ball

Answer 1

Given:
y= -x^2 - 2x + 24.

graph of an equation of the form y = ax² + bx + c ; a < 0, the parabola opens downward

a = -1 ; b = - 2 ; c + 24

x = 0 ; y = 0² - 2(0) + 24 ; y = 24   (0,24) y-coordinate

x = [-b + √(b² - 4ac)] / 2a 
x = [-(-2) + √(-2²) - 4(-1)(24)] / 2(-1)
x = [2 + √(4 + 28)] /  -2
x = [2 + √32] / -2
x = [2 + √(4*8)] / -2
x = [2 + 2 √8] / -2
x = 2 (1 + √8) / -2
x = 1 + √8 / -1

x = - 1 + √8  ; x = - 1 - √8
x = -1 + 2.83 ; x = -1 - 2.83
x = 1.83 ; x = -3.83

average:
1.83 + 3.83 = 5.66
5.66 / 2 = 2.83 midpoint

y = -(2.83)² - 2(2.83) + 24
y = - 8 - 5.66 + 24
y = 10.34

The maximum height of the ball is 10.34 feet.  (2.83,10.34)