Length of AB on Parabola 4x2+7x-1 - Find the Solution

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To find the length of segment AB on the parabola f(x) = 4x² + 7x - 1, where the origin is the midpoint, the coordinates of points A and B can be expressed as A(x_A, f(x_A)) and B(x_B, f(x_B)). The midpoint formula indicates that the coordinates of the midpoint are ((x_A + x_B)/2, (f(x_A) + f(x_B))/2). Setting the midpoint equal to the origin (0,0) leads to the equations x_A + x_B = 0 and f(x_A) + f(x_B) = 0. Solving these equations will yield the necessary values to calculate the length of AB.
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Homework Statement


points A and B are on the parabola f(x)=4xsquared + 7x-1, and the origin is the midpoint of AB, find the length of AB

Homework Equations





The Attempt at a Solution


I have spent time drawing out graphs and such but I am totally lost as to where to begin
 
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Start off by letting the coordinates be A(x_A,f(x_A)) and B(x_B,f(x_B)). Now, what would be the midpoint of of AB in terms of these coordinates?
 

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