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# Help me fast!

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1. There exist constants a, h, and k such that $$3x^2 + 12x + 4 = a(x - h)^2 + k$$
for all real numbers x. Enter the ordered triple (a,h,k)

2. Geometrically speaking, a parabola is defined as the set of points that are the same distance from a given point and a given line. The point is called the focus of the parabola and the line is called the directrix of the parabola.

Suppose $$\mathcal{P}$$ is a parabola with focus $$(4,3)$$ and directrix $$y=1$$. The point $$(8,6)$$ is on $$\mathcal{P}$$ because $$(8,6)$$ is $$5$$ units away from both the focus and the directrix.

If we write the equation whose graph is $$\mathcal{P}$$ in the form $$y=ax^2 + bx + c$$, then what is $$a+b+c$$?

Jul 2, 2020