Question

Describe the differences between the graph of y = –3(x + 7)^2 – 10 and the standard position graph of y = x^2.

Answer 1

y = –3(x + 7)^2 – 10

What you did was to reflect the y = x^2 graph about the x-axis. Then you shifted the new graph to the left by 7 units, increase the amplitude by a factor of 3 and moved the graph down by 10 units.

Answer 2

So these are the steps to get the y = –3(x + 7)^2 – 10 graph from the y = x^2 graph. Things in the bracket show what the steps account for.
1) Flip the graph about the x-axis once. [-]
2) Shift the graph to the left by 7 units. [x --> x+7]
3) Increase the amplitude by a factor of 3. [3]
4) Shift the graph down by 10 units [-10]

Answer 3

I dont know if the word amplitude applies here. I would say the graph is stretched vertically by a factor of three (or compressed horizontally by a factor of three)