Chapter 9, Problem 2SGR

To determine

To state if true or false.

Answer to Problem 2SGR

True

Explanation of Solution

Given information :

Vertex is the maximum or minimum point of parabola.

The graph of a quadratic equation ( $y=a{x}^2+bx+c$ ) is a parabola. The parabola is symmetric in nature and the point of symmetry is known as the vertex. This vertex lies on the line of symmetry and is symmetric about this line.

This vertex point shall be:

1. Highest point (if $a<0$) and be called the maximum. Here, the graph opens downwards.
2. Lowest point (if $a>0$) and be called the minimum. Here, the graph opens upwards.

A parabola always points to infinity, either negative or positive.

To graph a quadratic equation using table of values, compute the ‘y’ values for the corresponding ‘x’ values. For this, substitute the values of ‘x’ with negative as well as positive integers and check for the vertex.

Axis of symmetry for the given function is

  $x=-\frac{b}{2\times a}$

Therefore, it is true that the vertex is the maximum or minimum point of parabola.