Question 7 • [INMT3] Integrated Math 3 Sem 1 (26-27)
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 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.
Explanation
An equation has infinitely many solutions when both sides have the same value for every input, so their graphs overlap completely. Two quadratic expressions could be identical, such as x² + 1 = x² + 1, producing infinitely many intersection points. A constant and a linear or quadratic expression cannot have identical graphs for every input unless the other expression is also constant.
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