Heather is solving an equation by graphing the expressions on both sides. If her graph intersects at an infinite number of points, which statement could describe the equation Heather is attempting to solve?

Question

A. One side of the equation is a constant, and the other side of the equation is a linear expression.
B. One side of the equation is a linear expression, and the other side of the equation is a quadratic expression.
C. One side of the equation is a constant, and the other side of the equation is a quadratic expression.
D. One side of the equation is a quadratic expression, and the other side of the equation is a quadratic expression.

Answer 1

Since constants cannot intersect lines or parabolas in infinitely many points,

and lines cannot intersect parabolas in more than two points,

D is the only choice: the two expressions describe the same parabola.