Question

A) explain how to determine without graphing, whether the vertex of a quadratic function is a maximum or a minimum.

b) give an example of a quadratic function where the vertex is a minimum.
c) Give an example of a quadratic function where the vertex is a maximum

Answer 1

he vertex of a quadratic function is a maximum or minimum depending on the sign of the leading coefficient. If the leading coefficient is positive, the parabola opens upwards and the vertex is a minimum. If the leading coefficient is negative, the parabola opens downwards and the vertex is a maximum.

B) An example of a quadratic function where the vertex is a minimum is f(x) = x^2 + 2x + 1. The leading coefficient is positive, so the parabola opens upwards and the vertex is a minimum.

C) An example of a quadratic function where the vertex is a maximum is f(x) = -x^2 + 2x + 1. The leading coefficient is negative, so the parabola opens downwards and the vertex is a maximum.

Explanation: