Chapter 9.1, Problem 9P

Order each group of quadratic function from widest to narrowest graph.

$y=x^2,y=\frac{1}{3}{x}^2,y=2x^2$

To determine

To order the quadratic functions from widest to narrowest graph.

Answer to Problem 9P

The order of the quadratic function is $y=\frac{1}{3}{x}^2;y=x^2;y=2x^2$ .

Explanation of Solution

Given information:

The given quadratic functions are $y=x^2;y=\frac{1}{3}{x}^2;y=2x^2$ .

Graph:

  

Here, the red curve is the graph of $y=\frac{1}{3}{x}^2$ , green curve is the graph of $y=2x^2$ , blue curve is the graph of $y=x^2$ .

The given quadratic functions can be ordered as $y=\frac{1}{3}{x}^2;y=x^2;y=2x^2$ because smaller the value of the co-efficient of $x^2$ ,wider the graph.

Therefore, the order of the quadratic function is $y=\frac{1}{3}{x}^2;y=x^2;y=2x^2$ .