Write a new function 𝑔 given the following transformations from 𝑓(𝑥)= 3𝑥^2+ 2

Question

reflected over the x-axis and transformed right 2 and up 1

Answer 1

y = -(3x^2+2) reflects it about the x axis. All positive y's now become negative

It used to be an upward opening parabola with y intercept = 2. Now, it's a downward opening parabola with y intercept = -2

move it to the right by 2 means replace x by x-2

move it up by 1 means replace the y intercept of -2 by -1, just add 1 to the y intercept

y=-3(x-1)^2 -1 or

y=-3x+6x-4

Answer 2

Suggestion: you can see how the function changes at each step with a graphing calculator or a graphing application such as desmos.com

f(x) = 3x² + 2 given

-f(x) = -(3x² + 2) reflect about the x axis

-f(x - 2) = -(3(x - 2)² + 2 translate 2 right

-f(x - 2) + 1 = [-(3(x - 2)² + 2] + 1 translate up 1

g(x) = [-(3(x - 2)² + 2] + 1

Please do not try do simplify unless asked. If asked, compare results on a graphing utility.