# Finding Slope of a Tangent Line to a Parabola

Tags: line, parabola, slope, tangent
 P: 6 1. The problem statement, all variables and given/known data I've got the equation of a parabola $y=2x^2-4x+1$ with point (-1,7) and a tangent line running through it the point. I'm supposed to find the equation of the line. Simultaneously solve this equation with that of the parabola, place the results in form $ax^2+bx+c$, and find the slope of the tangent line. 2. Relevant equations $y=2x^2-4x+1$ $y=m(x--1)+7$ $ax^2+bx+c$ 3. The attempt at a solution I was supposed to find the equation of the line using the point slope equation and I did, I placed it above. The problem lies when I try to set the equations equal to each other $m(x+1)+7=2x^2-4x+1$and place the results in $ax^2+bx+c$ form. I guessed that $a=2$ and it was correct. However b is not $-4x-mx$ and c is not $m-6$
Since the line $y=m(x+1)+7$ passes through the point (-1,7) which we know is on the parabola, if we choose any real gradient other than the tangential gradient, it'll cut the parabola twice, while the tangent will cut the parabola once.