Originally posted by bard
1)Find equations of both lines through point (2,3) that are tangent to the parabola y=x^2+x.
2)The normal line to a curve c at a point Pis, by defininiton, the line that passes through p and is perpindicular to the tangent line c at P.
Where does the normal line to the parabola y=x^2x at point (1,0) intersect the parabola a second time?
3) Find a parabola with equation y=ax^2+bx+c that has slope 4 at x=1, slope 8 at x=1and passes through the point (2,15)
Thank You

I'll break the rules and get you started with the first one. The equation for a tangent line:
y=f'(a)(xa)+f(a)
You know,
3=f'(a)(2a)+f(a) holds for both lines
You also know,
f(a)=a^2+a
f'(a)=2a+1
So, 3=(2a+1)(2a)+a
^{2}+a