Question

Find the minimum value of the function:
f(x) = x2 + 9x – 16.

Answer 1

complete the square by halving the x coefficient and putting that in a squared bracket with x:

(x + 4.5)^2

This will give us an extra 20.25 we don’t want, so takeaway 20.25:

(x + 4.5)^2 — 20.25

Takeaway the 16 in the question:

(x + 4.5)^2 - 20.25 - 16 = (x + 4.5)^2 - 36.25

The minimum x coordinate is the number in the bracket with the opposite sign, thus the answer is -4.5 (the minimum y coordinate is the number outside the bracket with the same sign, -36.25)