Question

Please help,What is the range of the quadratic function
f(x) = -4x^2 + 16x + 2?

A. [18 ,infinty )
B. [2 , 18]
C. (-infinity , 18]
D. (- inifinity, 2]

Answer 1

parabola opens down because it is a negative function, max point is found using calculus, or calculator, the max point is the end point of your range, which is 18. so it will peak at 18 and continue back down for infinity. so (-inf,18]

Answer 2

max point can be found by making the derivitave of the slope of the function = 0

-8x+16=0
x=2 -----> plug 2 back into function to find y value, f(x) = -4(2)^2 + 16(2) + 2 = 18