are my values off because my leading coefficent was not 1 in the second equation?
There is an error some where with how the derivative is affecting the linear system; however, I can't find it so I solved your equation a different way.
We know the slope of the tangent line is 0 at (1,7); therefore, the general equation is .
If the parabola opens up, (-1,5) wouldn't be a point on the parabola.
So our equation becomes:
Now we have