What transformations take the parent function y = x² to y = -4( x - 7)²?
5 points
vertical stretch by a factor of -4, horizontal shift left 7 units.
x-axis reflection, vertical stretch by a factor of 4, horizontal shift left 7 units.
vertical stretch by a factor of -4, horizontal shift right 7 units.
x-axis reflection, vertical stretch by a factor of 4, horizontal shift right 7 units.

D

Step-by-step explanation:

Let's look at the easy part: we see that the new equation has a negative at the front. A negative sign indicates a reflection. Since this negative sign is on the entire equation instead of just on the x, we know it's a vertical reflection; in other words, it's a reflection over the x axis.

Eliminate the choices that don't include reflection: A and C are gone.

We have B and D left. Now, look at the x - 7 part of the new equation. Here, we see that the graph has shifted horizontally either right or left. We know it's shifted right because of the negative sign. For horizontal transformations, things are a little backwards: - means right and + means left. So, eliminate B because that's wrong.

Thus, D is the answer.

Hope this helps!

x-axis reflection, vertical stretch by a factor of 4, horizontal shift right 7 units.

Step-by-step explanation:

y = x² to y = -4( x - 7)²

x² to (x-7)²

7 units towards right

4(x-7)²

Vertical stretch of factor 4

-4(x-7)²

Reflection in the x-axis