Chapter 9, Problem 3PT

To determine

To evaluate if the function has a minimum or maximum value

Answer to Problem 3PT

The function has a minimum value.

Explanation of Solution

Given information :

The function provided is :- $y=x^2-7x+6$

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.

Here, a is greater than zero, hence the parabola opens upwards, and has a minimum value.

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.

Therefore, the function $y=x^2-7x+6$ has a minimum value.