Question

How do you use the important points to sketch the graph of `y= 2x^2`?

Answer 1

Please see the explanation.

Explanation:

Given:

`color(blue)(y=2x^2 " "` Input Function

A quadratic function has a general form:

`color(red)(f(x) = ax^2+bx+c`

Referring to the Input Function that we have,

`a = 2; b = 0 and c=0`

Vertex of a quadratic function in general form

`Vertex: (-b)/(2a`

`Vertex: (-0)/(2(2)] = 0`

This value is the x coordinate of our vertex.

To find the y coordinate value of our vertex, substitute in our Input Function

`y=2(0)^2=0`

Hence, our Vertex is at `(0,0)`

Using a spreadsheet software, we can enter some values for `x` and find the corresponding y values:

Refer to the image of the graph available below to comprehend the behavior of `color(blue)(y=2x^2 " "`