Question

The roots of the equation $x^2-2x=0$ can be obtained graphically by finding the abscissas of the points of intersection of each of the following pairs of equations except the pair:

$y=x^2,$ $y=2x$

$y=x^2-2x,$ $y=0$

$y=x,$ $y=x-2$

$y=x^2-2x+1,$ $y=1$

$y=x^2-1,$ $y=2x-1$

Answer: C

Concepts:function quadratic algebraic manipulation

Difficulty rating: 1320

Small Hint:

Set the two right-hand sides in each pair equal

Big Hint:

Four pairs reduce to $x^2-2x=0$ ; one pair reduces to an impossible constant equation

Solution:

Choices A, B, D, and E all reduce their intersection condition to $x^2-2x=0.$ Choice C instead requires $x=x-2,$ which has no solution and therefore cannot produce the desired roots.

Thus, the correct answer is C.

1951 AMC 12 Problem 33

Answer: C

Difficulty rating: 1320

Small Hint:

Big Hint:

Solution:

Problem 33 in Other Years