PLEASE HELP ASAP! Thanks!!!!! Explain:
1 answer:
Answer:
(3, 3) and (15, 15)
Step-by-step explanation:
The points equidistant from the given point and the y-axis lie on the parabola that has (3,6) as its focus and the y-axis as its directrix. The equation for that can be simplified from ...
(x -3)^2 +(y -6)^2 = x^2
-6x +9 +y^2 -12y +36 = 0 . . . . . subtract x^2, eliminate parentheses
We can find the points that lie on the line y=x (equidistant from both axes) by substituting y for x or vice versa. Then we have the quadratic ...
x^2 -18x +45 = 0 . . . . substitute x for y and collect terms
(x -3)(x -15) = 0 . . . . factor it
x = 3 or 15
So, the points of interest are (x, y) = (3, 3) and (x, y) = (15, 15).
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Answer:
(-1, 6)
Step-by-step explanation:
A graphing calculator shows the vertex to be (x, y) = (-1, 6).
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You can also find it by putting the equation into vertex form.
y = -2(x^2 +2x) +4
y = -2(x^2 +2x +1) +4 +2(1) . . . . . add 1 inside parens; the opposite outside
y = -2(x +1)^2 +6
Compare to ...
y = a(x -h)^2 +k
and you see a=-2, h=-1, k=6
The vertex is (h, k) = (-1, 6).
