Chapter 8.1, Problem 2E

To determine

To state:When does the graph of a quadratic function open up and open down

Answer to Problem 2E

The graph of a quadratic function opens up when it is of the form $y=f{(x-a)}^2$ where a is any constant.

The graph of a quadratic function opens down when it is of the form $y=-f{(x-a)}^2$ where a is any constant.

Explanation of Solution

Given: A quadratic function

A quadratic function is generally of the form $y=\pm f{(x-a)}^2$ or, $x=\pm f{(y-a)}^2$ where a is any constant. This kind of a graph is called a parabolic curve.

The graph of a quadratic function opens up when it is of the form $y=f{(x-a)}^2$ . For example let us consider the graph of $y={(x-1)}^2$ which is open upwards and is given by

  

The graph of a quadratic function opens down when it is of the form $y=-f{(x-a)}^2$ . For example let us consider the graph of $y=-{(x-1)}^2$ which is open upwards and is given by