9. Think about the standard parabola defined by 𝑦 = 𝑥2. How does the parabola defined by 𝑦 = −4(𝑥 + 3)2 − 7 compare to the standard parabola? Describe all of the transformations. Then, draw a reasonable sketch of both parabolas.

Answer 1

The parabola defined by 𝑦 = −4(𝑥 + 3)2 − 7 is the standard parabola 𝑦 = 𝑥2 that has undergone a few transformations.

First, the entire graph has been shifted three units to the left (because of the (𝑥 + 3) term inside the parentheses).

Next, the parabola has been stretched vertically by a factor of 4 (because of the coefficient -4 in front of the parentheses).

Finally, the parabola has been shifted seven units downward (because of the -7 added at the end).

A rough sketch of the two parabolas would look like this: