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

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In summary, the equation for finding the length of AB on a parabola is 4x^2 + 7x - 1, where x is the distance along the parabola. To calculate the solution for the length of AB, you will need to use this equation and plug in the value for x. The length of AB cannot be negative as it represents the distance along the curve. The position of the parabola does affect the length of AB, but the coefficient and constant term in the equation do not.
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chillfactor
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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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  • #2
Start off by letting the coordinates be [tex]A(x_A,f(x_A))[/tex] and [tex]B(x_B,f(x_B))[/tex]. Now, what would be the midpoint of of AB in terms of these coordinates?
 

1. What is the equation for finding the length of AB on a parabola?

The equation for finding the length of AB on a parabola is 4x^2 + 7x - 1, where x is the distance along the parabola.

2. How do you calculate the solution for the length of AB?

To calculate the solution for the length of AB, you will need to use the equation 4x^2 + 7x - 1 and plug in the value for x. This will give you the length of AB in units.

3. Can the length of AB on a parabola be negative?

No, the length of AB on a parabola cannot be negative. It represents the distance along the curve, which is always a positive value.

4. Is the length of AB on a parabola affected by the position of the parabola?

Yes, the length of AB on a parabola is affected by the position of the parabola. If the parabola is shifted horizontally or vertically, the length of AB will change accordingly.

5. Are there any other factors that can affect the length of AB on a parabola?

No, the length of AB on a parabola is only affected by the position of the parabola. The coefficient and constant term in the equation do not affect the length of AB.

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