Graphing a Parabola in Vertex Form

Vertex form is different from standard form, it looks like: y = 2(x - 3)^2 + 4. The 3 inside the parentheses tells us where to move on the x-axis, but the OPPOSITE because it's inside parentheses. The 4 at the end tells us where to move on the y-axis (not opposite because it's not inside parentheses). Together, (3, 4) makes the vertex of the parabola.

We can treat the 2 on the outside of the parabola like a slope. From your vertex, go up 2, over one on both sides of the function. Connect them with a curve at the bottom to make your parabola.

There are a few special cases that we should note:

y = 1/2(x + 3)^2 + 3 - the 1/2 in front of the parentheses tells us the parabola will get wider, not thinner.
y = (x + 3)^2 - this means the vertex will remain on the x - axis
y = 3x^2 + 1 - this means the vertex will remain on the y-axis
y = x^2 - when there are no numbers, the parabola remains on the origin of the coordinate plane.