How do I work this problem?

Question

Start with the function f(x) = x^2
. Through translations, reflections, stretching and shrinking, arrive at the function
g(x). Use these steps to help graph g(x) as well.

 

g(x) = −2x^2 + 12x − 14

Answer 1

You need to put g(x) in vertex format by completing the square:

 

g(x) = -2(x² - 6x + 9) - 14 + 18

 

g(x) = -2(x-3)² + 4

 

The translations are:

 

3 to the right, 4 up, stretch by a factor of 2, and reflected over the x-axis