Solving One-Variable Equations with Systems — Quiz
Question 6 • Mathematics III
Heather is solving an equation by graphing the expressions on either side of the equal signs. If the graph intersects at an infinite number of points, which statement could describe the equation Heather is attempting to solve?
Answer
A
One side of the equation is a linear expression, and the other side of the equation is a quadratic expression.
B
One side of the equation is a constant, 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 linear expression.
D
One side of the equation is a quadratic expression, and the other side of the equation is a quadratic expression.
Explanation
An infinite number of intersection points means the two graphs are the same at every input. That can happen when both sides are quadratic expressions with matching coefficients, such as x² + 2x = x² + 2x. A constant and a linear or quadratic expression, or a linear and a quadratic expression, do not describe the same graph for all inputs in general.
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