SOLUTION: find the y-k=a(x-h)^2 equation for the parabola with vertex = (-2,6) and y-intercept = -2

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Question 731342: find the y-k=a(x-h)^2 equation for the parabola with vertex = (-2,6) and y-intercept = -2
Found 2 solutions by josgarithmetic, MathLover1:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Each of those points gives you a specific equation, so you could have two of them.

a%28x-h%29%5E2%2Bk=y will be our best form to start with (my convenience only).

Point (-2, 6):
a%28-2-h%29%5E2%2Bk=6
and since the point is also the vertex,
a%28-2%2B2%29%5E2%2Bk=6
a%2A0%2Bk=6
0%2Bk=6
k=6.

That point being vertex lets us find a%28x%2B2%29%5E2%2B6=y, so now we only have one unknown variable in the equation other than the general (x, y) variables.

The other given point is (0, -2):
a%280%2B2%29%5E2%2B6=-2
4a%2B6=-2
4a=-2-6
4a=-8
a=-2

Equation for the parabola is highlight%28y-6=-2%28x%2B2%29%5E2%29

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given:
vertex = (-2,6) and y-intercept+=+-2
Step 1:
The standard equation of parabola when the vertex is along y intercept is given by:
+%28x-h%29%5E2=4p%28y-k%29 where vertex:(h,k) = (-2,6)
and p=+y-intercept+=+-2
Step 2:
Putting values of h, k and p in the standard equation and simplifying you get:

%28x-%28-2%29%29%5E2+=4%28-2%29%28y+-+6%29
%28x%2B2%29%5E2+=-8%28y+-+6%29

x%5E2+%2B+4x+%2B+4+=+-8y+%2B+48
8y+=-x%5E2+-4x+%2B44+
y+=%28-1%2F8%29x%5E2+-%281%2F2%29x+%2B11%2F2+is the required equation of parabola.This is the answer.