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?
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.
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.
B. One side of the equation is a linear expression, and the other side of the equation is a quadratic expression.
To determine the correct statement that describes the equation Heather is attempting to solve, we need to understand the meaning of intersecting at an infinite number of points on a graph.
When two expressions intersect on a graph, it means there is a point where the values of the expressions are equal. In other words, the equation is satisfied at that point.
If the graph intersects at an infinite number of points, it implies that the two expressions are always equal, regardless of the values of the variables. This situation occurs when one side of the equation is a constant and the other side is a linear expression.
Considering this information, the correct statement is:
A. One side of the equation is a constant, and the other side of the equation is a linear expression.