Chapter 9, Problem 4SGR

To determine

The graph of a quadratic function has maximum if the coefficient of the $x^2$ is positive

Answer to Problem 4SGR

False, the graph of a quadratic function has maximum if the coefficient of the $x^2$ is positive

Explanation of Solution

Given:

The vertex is the maximum or minimum point of a parabola.

Concept Used:

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

True statement: The graph of a quadratic function has maximum if the coefficient of the $x^2$ is negative.

So, the graph of a quadratic function has maximum if the coefficient of the $x^2$ is positive is a false statement.

Thus, the vertex is the maximum or minimum point of a parabola is always true.