# Calc problems

## Main Question or Discussion Point

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^2-x 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

sol1
Late Bloomer

I have much to learn, and the converstaion is ahead of my knowledge but I am interested to follow as best I can. Sorry for intrusion.

Sol

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^2-x 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)(x-a)+f(a)
You know,
-3=f'(a)(2-a)+f(a) holds for both lines
You also know,
f(a)=a^2+a
f'(a)=2a+1
So, -3=(2a+1)(2-a)+a2+a

HallsofIvy