Chapter 9.1, Problem 5LC

To determine

The situations when the vertex of the parabola is at minimum and maximum point.

Answer to Problem 5LC

When the $a>0$ , the graph of $a{x}^2+bx+c$ opens upward. Hence, the vertex is a minimum point.

When the $a<0$ , the graph of $a{x}^2+bx+c$ opens upward. Hence, the vertex is a maximum point.

Explanation of Solution

The parabola is graph of a quadratic function:

  $a{x}^2+bx+c$

The parabola is nothing but a U shaped curve and the extreme points on this parabola are called the vertex of the parabola.

When the $a>0$ , the graph of $a{x}^2+bx+c$ opens upward. Hence, the vertex is a minimum point.

When the $a<0$ , the graph of $a{x}^2+bx+c$ opens upward. Hence, the vertex is a maximum point.