1. The problem statement, all variables and given/known data Hi! I am doing some problems to practice for a math competition, and I'm wondering if I did this correctly. I don't really have an answer sheet, so I have no way of knowing whether I'm right. If you would please review it, that would be cool! It reads: There are exactly two values of m for which the line y=mx-12 is tangent to the parabola y=x^2-3x+5. Determine those two values. 2. Relevant equations y=mx-12 y=x^2-3x+5 3. The attempt at a solution Okay so first I found the derivative of y=x^2-3x+5. y'=2x-3 This is the slope, so I put it into the equation of the tangent line: y=mx-12=(2x-3)x-12=2x^2-3x-12 <-- the tangent line Now I made the the two equations equal to each other because they intersect at one point, right? so: x^2-3x+5=2x^2-3x-12 and when I solve for x it gives me +/- √17 I put this into the equation for the slope and I get: m= 2√17 -3 or m=-2√17 -3 Is this correct? Thank you in advance.