You have the vertex, and so we have y=a(x-h)^2 + k
(h,k) is the vertex, while (x,y) can just be a random point
we need to solve for a
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snowflake0531:
You did a couple of problems before this, hopefully, you'll know hwo to solve for a, after you get that
expand the form of a(h-k)^2 + k
to get standard form -> ax^2 + bx-c
surjithayer:
let the eq. of parabola be
y=ax^2+bx+c
it passes through (-1,2),(3,2) and (1,-2)
2=a-b+c ...(1)
2=9a+3b+c ...(2)
-2=a+b+c ...(3)
(3)-(1) gives
-2-2=b+b
2b=-4,
b=-2
(2)-(1) gives
0=8a+4b
0=2a+b
2a=-b=-(-2)
a=2/2=1
from (1)
2=1+2+c
c=-1
so
y=x^2-2x-1
https://www.desmos.com/calculator/xjzkiefn3p
y=x^2-2x-1