1965 AMC 12 Problem 9

Attempt Problem 9 of the 1965 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 1965 AMC 12 solutions, or check the answer key.

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

The vertex of the parabola

y=x^2-8x+c

will be a point on the

x

-axis if the value of

c

is:

-16

-4

4

8

16

Complete the square in

x^2-8x+c

The vertex’s

y

-coordinate must equal

0

Completing the square gives

y=(x-4)^2+c-16.

The vertex is

(4,c-16),

so it lies on the

x

-axis when

c=16.

Therefore, the correct answer is E.

Problem 9 in other years