Chapter 9, Problem 3PT

To determine

Define the function $y=x^2-7x+6$ has a minimum or maximum value.

Answer to Problem 3PT

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

Explanation of Solution

Given:

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

Concept Used:

If the coefficient of $x^2$ is positive, then the graph of the parabola is upward open and vertex is at minimum.

If the coefficient of $x^2$ is negative, then the graph of the parabola is downward open and vertex is at maximum.

The graph of any quadratic function is a parabola.

$y=a{x}^2+bx+c$(a is positive) − minimum	$y=-a{x}^2+bx+c$(a is negative) − maximum

The function $y=x^2-7x+6$ , the coefficient of $x^2$ is positive; it is upward open, so it has a minimum value.

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