Question

What is the equation of the graph below?

(3 points)
y = –1(x – 2)2 + 3
y = 1(x + 2)2 + 3
y = –1(x + 3)2 + 2
y = 1(x – 3)2 + 2

Answer 1

It's the last one!
So you are studying transformations right?
If I have the form y =x^2, I have a parabola. That is the general shape that is on the graph. If it is simply y = x^2, then the tip of the parabola touches the origin.
If I want to shift it up and down, I simply append that desired change to the right side of the equation. In our case, the graph moves up 2 units from the original,
xo y = x^2 + 2
However, we also see a shift tot the right by three units.
This is sort of tricky because it's backwards. If you move right 3, you subtract 3 from the x.
so y = (x-3)^2 + 2
And the times positive one is because it does not flip upside down.

In other words:
y = (x+b)^2 + a
A = vertical shift. + is up, - is down
B = horizontal shift. + left, - is right.