Question

Drag the labels to the correct locations. Each label can be used more than once, but not all labels will be used. Let’s look back at the same quadratic functions you saw in the Warm-Up at the beginning of this lesson. Use what you learned about the fundamental theorem of algebra to determine the number of real and complex roots each function has. two distinct real rootsone repeated real rootone real root and one complex roottwo complex roots

Answer 1

Graph A: two distinct roots. Graph B: one repeated real root. Graph C: two complex roots. Graph D: two distinct real roots.

Explanation:

Explanation:

Each graph represents a quadratic function. So by the fundamental theorem of algebra, we know that each graph will have two roots.

Graph A crosses the x-axis twice. So, graph A has two distinct real roots.

Graph B touches the x-axis once. A quadratic cannot have one real root and one complex root. So it must have one repeated real root.

Graph C doesn’t cross the x-axis. This means it must have two complex roots.

Graph D crosses the x-axis twice. So, graph D has two distinct real roots.