Question

Which statements describe one of the transformations performed on f(x)=x^2 to create g(x)=3(x+5)^2-2?
A. A translation of 5 units to the left.
B. A translation of 2 units to the left.
C. A vertical stretch with a scale factor of 3.
D. A vertical stretch with a scale factor of 1/3.

Answer 1

Hint:
From f(x)=x^2 (or any other function)
g(x)=f(x-h)+k, where h,k \(\in R\), i.e. h & k are real numbers.
means
translation to the right if h>0
translation to the left if h<0
translation upwards if k>0
translation downwards if k<0.

Example:
f(x)=x^2+3x
g(x)=f(x-3)+7 ...... h=3, k=7, ....translating 3 units right, 7 units up.
=(x-3)^2+3(x-3) + 7
= x^2-3x+7

Answer 2

Thanks!