Given the quadratic function f(x) = 16x2 – 64x + 64, find a value of x such that f(x) = 16.

Answer 1

f(x) = 16x2 – 64x + 64
for f(x)=16, write:
16=16x² - 64x +64
transpose 16 to the right, and factor out numeric factor 16:
16(x² -4x +3) = 0
Factor expression
16(x-3)(x-1)=0
This means that x=3 or x=1, either one of which satisfies the equation
f(x)=16.

Check by substituting x=3 or x=1 in f(x).