I can't remember how to tackle this type of question, I don't need the answer, just the steps.

Find the y-intercept of the parabola with a vertex of (-5,2) that passes through (-4,5)

Well, I don't know how you would do it, but I would have used the completed square formula to solve this.

The completed square form of a general quadratic is [math]y = a(x + \frac{b}{2a})^2 - \frac{b^2}{4a} + c[\math]

The vertex is given by

That means, and

Then, using your given point, you have another equation;

You should be able to solve for a, b and c, then, set x to zero in your equation to have the y intercept.