Question

Find the equation of the tangent to the parabola y = x^2 − 5x − 3 that is parallel to the line 3x − y − 7 = 0.

Answer 1

Are you allowed to use calculus or is this algebra?

Answer 2

algebra preferred

Answer 3

I mean, it's much harder without calculus lol.

Answer 4

So you want it tangent to that parabola, that means you need to realize certain things. When you draw out the two lines, they will look something like this.


Keep in mind this is a generic representation, I don't actually know what either of them look like, but you get the idea.

So you're making a line. Can you draw the line on there that you want to make?

Answer 5

I think there are some techniques for doing this sort of thing without calculus lol, similar to techniques for calculating the volumes of solids with out definite integrals

Answer 6

Just use my example and show me what your line will look like. Remember, it's tangent to the parabola and parallel to the straight line.