Understanding the algebra problem

Question

A ball is thrown upward and outward from a height of 6 feet. The height of the ball, 𝑓(𝑥), in feet, can be modeled by 𝑓(𝑥) = −0.6𝑥^2 + 2.7𝑥 + 6 where 𝑥 is the ball’s horizontal distance, in feet, from where it was thrown. Check your solutions.

Answer 1

h(x)=-.6x^2 +2.7x+6

h'= -1.2x +2.7=0

x=27/12= 9/4=2.25 feet out, when height is maximum

max height = -.6(2.25)^2 +2.7(2.25)+6= 9.0375 feet high

it hits the ground when -.6x^2 +2.7x +6 = 0

or when

2x^2 -9x -20 = 0

use the quadratic formula, complete the square or factor

x = 9/4 +/- .25sqr(81+160)

= 2.25 +.25sqr241

= about 2.25+ 15.52/4

= 2.25+3.88

= 6.13 feet out

the ball follows a parabolic arc

with vertex = max height f(2.25) = (x, f(x)) = (2.25, 9.0375)