Question 184808
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I have been working on this math problem and I can't seem to figure it out. I was wondering if someone could help me? 
Please and Thank You!! I would deeply appreciate it!!

Find all intercepts of the parabola y-2=-1/2(x-4)^2

TOTALLY, TOTALLY UNNECESSARY steps by the person who responded.

{{{y - 2 = (- 1/2)(x - 4)^2}}}
{{{y = (- 1/2)(x + highlight(- 4))^2 + highlight_green(2)}}} ----- Adding 2 to both sides
{{{y = a(x + highlight(- h))^2 + highlight_green( k)}}} ----- Vertex form of a parabola, where the VERTEX, (h, k) = (4, 2)
"h" is the x-coordinate of the vertex of the parabola, is also the paeabola's Axis of Symmetry, as well as the MIDWAY point
between the x-intercepts.
If MiDWAY between 2 points of a HORIZONTAL line is 4, then LEFT and RIGHT endpoints are: {{{4 - 4/2 = 4 - 2 = 2}}}, and {{{4 + 4/2 = 4 + 2 = 6}}}.
Therefore, x-intercepts are 2 and 6, or at the coordinate points: (2, 0) and (6, 0).


Although more time-consuming, we can also do the following:
{{{y - 2 = (- 1/2)(x - 4)^2}}}
{{{y = (- 1/2)(x - 4)^2 + 2}}} ---- Adding 2 to both sides
{{{y = (- 1/2)(x^2 - 8x + 16) + 2}}}
{{{0 = (- 1/2)(x^2 - 8x + 16) + 2}}} ---- Substituting 0 for y, since y-values on x-axis are 0
- 2(0) = {{{- 2((- 1/2)(x^2 - 8x + 16) + 2))}}} ---- Multiplying each side by - 2
{{{matrix(1,3, 0 = x^2 - 8x + 16 - 4, or, x^2 - 8x + 12 = 0)}}}
(x - 2)(x - 6) = 0 ---- Factorizing the trinomial
x - 2 = 0       OR      x - 6 = 0
x = 2           OR      x = 6
x-INTERCEPTS: (2, 0) (6, 0)</pre>