SOLUTION: Write the equation for the parabola which opens left, has its vertex on the origin, and passes through the point (-3/2),1)

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Question 366722: Write the equation for the parabola which opens left, has its vertex on the origin, and passes through the point (-3/2),1)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
It would be of the form x+=+-ay%5E2+%2B+by+%2B+c
If the vertex is at the origin, then I can write
0+=+-a%2A0+%2B+b%2A0+%2B+c, so c+=+0
If it includes (-3/2,1),
-3%2F2+=+-a%2A1%5E2+%2B+b%2A1
(1) b+-+a+=+-3%2F2
By symmetry, it must also pass through (-3/2,-1), so
-3%2F2+=+-a%28-1%29%5E2+%2B+b%2A%28-1%29
(2) -b+-+a+=+-3%2F2
Add (1) and (2)
-2a+=+-3
a+=+3%2F2
And, since
(1) b+-+a+=+-3%2F2
b+=+-3%2F2+%2B+a
b+=+-3%2F2+%2B+3%2F2
b+=+0
The equation is
x+=+-%283%2F2%29%2Ay%5E2