SOLUTION: PLEASE ANSWER ASAP!!!! Points A and B are on a parabola y = 4x^2+ 7x -1 and the origin is the midpoint of AB. ***What is the length of AB? THANK YOU!!!

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Let A = (xo,yo) ,B = (x1,y1),then their midpoint is
((xo+x1)/2,(yo+y1)/2) = (0,0).
So x1=-x0,y1=-yo.

Since A,B are both on the the parabola,
we have yo = ...(1) and
-yo = ...(2)

(1)+(2): 0 =
So, xo = 1/2 or -1/2
and hence,yo = 4(1/4) - 7/2 - 1= -7/2
or yo = 7/2

Let O be the origin.
We see that the length of AB = 2 distance of OA
= 2
= 2
=
Kenny