Everything I need to know about quadratic forms

Which is the standard form of a quadratic function?

Which is the factored / intercept form of a quadratic function?

Which is the vertex form of a quadratic function?

When is a parabola concave up?

When is a parabola vertically stretched / narrower?

When is a parabola vertically shrunk / wider?

When is a parabola concave down?

How do you find the axis of symmetry from standard form?

How do you find the axis of symmetry from vertex form?

How do you find the axis of symmetry from factored / intercept form?