- 19

- 0

**1. Homework Statement**

Two points are located on the graph [tex]y=4x^{2}+7x-1[/tex]. A line drawn between these two points have a mid-point at (0,0). Find these two points.

**2. Homework Equations**

The midpoint formula [tex](x_{m},y_{m})=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]

**3. The Attempt at a Solution**

I have worked out the distance from a point on the graph to the origin as a function of x [tex]d=\sqrt{16x^{4}+56x^{3}+42x^{2}-14x+1}[/tex], by plugging in the parabolic equation into the [tex]d=\sqrt{x^{2}+y^{2}}[/tex]. I have also figured out these set of rules for [tex]x_{1}, x_{2}, y_{1}[/tex] and [tex]y_{2}[/tex]:

[tex]x_{1}+x_{2}=0[/tex] and [tex]y_{1}+y_{2}=0[/tex]

Thus [Tex]x_{1}= -x_{2}[/tex] and [tex]y_{1}= -y_{2}[/Tex]

All of the above were derived from the midpoint formula, since the mid-point is (0,0), both the x's and the y's have to cancel out each other.

Thanks in Advance!