Question

A ball is thrown upward from the top of a building. The function below shows the height of the ball in relation to sea level, ft, in feet, at different times t in seconds:

f(t) = -16t2 + 32t + 90

The average rate of change of f(t) from t = 4 seconds to t = 6 seconds is _____ feet per second.

Answer 1

Solve
2x2−12x+5=0

pattern match this equation with
ax2+bx+c=0

we see a=2, b= -12 , and c= 5
use those numbers to replace a,b, and c in the quadratic formula
x=−b±b2−4ac−−−−−−−√2a

notice we use the discriminant, which you know how to find.
b2−4ac becomes 144 - 4*2*5= 144-40= 104

x=12±104−−−√2⋅2124±226−−√4x=3±1226−−√


if we put one of these solutions into the original equation we will get zero (just as we should)

Answer 2

https://www.khanacademy.org/math/algebra/quadratics/quadratic-formula/v/using-the-quadratic-formula

Answer 3

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