Chapter 9.3, Problem 41STP

To determine

Find the option which describes the graph of $y=2x^2$

Answer to Problem 41STP

Option D is correct.

Explanation of Solution

Given:

The function: $y=2x^2$

Concept Used:

An equation in the form $y=a{x}^2$ is a quadratic equation whose graph is a parabola.

So, choice A cannot be correct as a line would have a linear equation in the form $y=mx+b$ .

For $y=2x^2,a=2$ since the value of a > 0 (positive), this parabola opens up and thus has a minimum at (0, 0), and it cannot be wider.

Rule if a > 1 vertically stretched by a factor of a. It should be narrower.

Therefore, choice B and C can be eliminated.

Since $a=2$ , this function is a dilation of the graph of $y=x^2$ that is stretched vertically. A parabola that is stretched vertically will become narrower.

So D is the correct choice.

Thus, option D is correct.