Question

How to determine if a minimum or maximum from a quadratic.

A) Discriminant is positive
B) Discriminant is negative
C) Vertex is at the origin
D) Vertex is at a maximum

Answer 1

To determine if a quadratic function has a minimum or maximum, consider the discriminant, the vertex, and the concavity of the graph.

Step-by-step explanation:

To determine if a quadratic function has a minimum or maximum, you can consider the discriminant, the vertex, and the concavity of the graph.

A) If the discriminant (b^2 - 4ac) is positive, the quadratic has two distinct real roots and the graph opens upwards, indicating a minimum point.

B) If the discriminant is negative, the quadratic has no real roots and the graph either opens downwards or upwards, but in either case, it does not have a minimum or maximum point.

C) If the vertex is at the origin (0,0), the quadratic has a minimum point.

D) If the vertex is at a maximum, the quadratic has a maximum point.