Which of the following transformations is performed on the parabola f(x) = 2x^2 ?

Question

Which of the following transformations is performed on the parabola f(x) = 2x²?

 horizontal translation

vertical compression

vertical stretch

vertical translation

Answer 1

Translations would be if the parabola vertex moves away from the point of origin. That would mean we would add/subtract in some way:

x² + c would move the parabola up/down

(x + c)² would move the parabola left/right

We don't have either of these, so it's not a translation.

We do, however, have a coefficient on our squared variable. To tell if it's stretch or compressed rmember the following:

If |a| > 1, then stretch

If 0 < |a| < 1, then compression

That is, if the absolute value of the coefficient is greater than 1, then it's a stretch. If the absolute value is between 0 and 1, then it's a compression

Example. Let's make x = 4, and compare the baseline coefficient of 1 versus 2 and ¹/₂:

1 * 4² = 1 * 16 = 16

2 * 4² = 2 * 16 = 32

¹/₂ * 4² = ¹/₂ * 16 = 8

At the 1 coefficient, we have our control point at 16. When we made that coefficient a 2, that number spiked up to 32, while the ¹/₂ pressed the value down to 8.