Question

Algebra homework packet answer for 50 points.

Answer 1

The standard form for a parabola is (x - h)2 = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y - k)2 = 4p (x - h), where the focus is (h + p, k) and the directrix (d)
is x = h - p.
So directrix is: y = k - p and the focus is at:
(h, k+p)
Since our focus is: (1, 3) and directrix is: y = 1,
thus h = 1, k+p = 3, and k-p = 1
Therefore k = 3-p, 3-p-p = 1, k = 3-p = 3-1 = 2
3-2p = 1, -2p = -3+1, -2p = -2, p = 1
Now we plug p, k, & h into standard form:
(x - h)2 = 4p (y - k)
${(x - 1)}^{2} = 4(1)(y - 2) \\ {(x - 1)}^{2} = 4y - 8 \\ 4y = {(x - 1)}^{2} + 8 \\ y = ({(x - 1)}^{2} \div 4) + 2$
y = 1/4 (x-1)^2 + 2