1955 AMC 12 Problem 24

Attempt Problem 24 of the 1955 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1955 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

24.

The function

4x^2-12x-1:

always increases as

x

increases

always decreases as

x

decreases to

1

cannot equal

0

has a maximum value when

x

is negative

has a minimum value of

-10

Complete the square in

4x^2-12x-1

Factor

4

from the quadratic terms before forming

(x-\frac{3}{2})^2

Completing the square,

\begin{aligned} 4x^2-12x-1 &=4\left(x-\frac32\right)^2\\ &\quad{}-10. \end{aligned}

The squared term is nonnegative, so the minimum value is

-10,

attained at

x=\frac{3}{2}.

Thus, the correct answer is E.

Problem 24 in other years