Between e, and f how do I know whether to use y= a(x-h)^2+k form, or ax^2 +bx +c form? And how do I work it out?
And how do I work out this one step by step?
to #3:
All points on the x-axis have the y-coordinate zero. Thus you know 2 points of the parabola:
P(-1, 4), Q(6, 0) . Plug in these coordinates into the given equation. You'll get a system of linear equations. Solve for a and b:
$\displaystyle \left|\begin{array}{l}4 = a - b\\0 = 36a+6b\end{array}\right.$ ...... I've got $\displaystyle (a, b) = \left(\frac47, -\frac{24}{7}\right)$
If you know the coordinates of the vertex the equation $\displaystyle y= a(x-h)^2+k$ would be the best.
In both cases you know the coordinates of the vertex and the coordinates of one additional point. I'm going to do f so you can try to do e:
You know: V(2, 2) and P(0, 6). Plug in these coordinates:
$\displaystyle 6 = a (0 - 2)^2 + 2~\implies~ 6 = 4a+2~\implies~a = 1$ . Thus your equation becomes:
$\displaystyle y = (x-2)^2+2$