# Yahoo Answers 06-19-14 - 2

- Author:
- Michael Brown

- Topic:
- Parabola, Translation

Equation of quadratic that has been horizontally by 3 and reflected over the y axis and translated 3 up.?
Since it's horizontally 3, I'll assume that's 3 to the right
You can use any values for a, h and k you want (as long as a is not 0)
I'm also using the vertex form so it's easier to see the movements. You could convert it to standard form but it's not as apparent what is happening.
Quadratic:
y=a(x-h)^2+k or f(x)
shifted 3 units to the right
y=a(x-h-3)^2+k or g(x)=f(x-3)
reflected over the y-axis means x=-x
y=a(-x-h-3)^2+k or h(x)=g(-x)
look at what happens... -x-h-3=-1(x+h+3) and when you square -1 it goes away but the x coordinate of the vertex has flipped from one side to the other
translated 3 up
y=a(x+h+3)^2+k+3 or j(x)=h(x)+3
Here's a graph with some random numbers. Change f(x) and watch how the rest changes.