Relations in Standard, Factored, and Vertex Form.

I'm having trouble understanding some work I'm doing.

I'm having trouble transitioning relations to different forms.

For Example, taking a factored form, putting into standard, then vertex.

Are there any tips you could give me to help me understand how to do this?

Here are some example questions.

Write the following in standard form: y = 5(x+3)^2 -2

Write the following in vertex form: y = 3x^2 + 12x

Solve the following quadratic: 3x^2 - 24x + 48 = 0

Find in vertex form, the equation of the quadratic relation with a vertex at (6,2) a nd passing through (3,20).