Question

Find k such that y=k-x^2 is tangent to y=-6x+7

Answer 1

solve both the equations

Answer 2

i know the derivative of the second one is -6 but i dont know where to go from there

Answer 3

Since the slope of the tangent line is -6, set the derivative of the first equation to -6...
ie,
-2x = -6
x = ???

Answer 4

^^ that is the x-coordinate where tangency occurs.

Answer 5

x=3 is not the answer though. i just tried it. they are looking for k

Answer 6

k=-2 right? (trying to follow along)

Answer 7

I know... we're not done yet....

Answer 8

yes it is -2! how did you find that

Answer 9

At that x coordinate, find the y-coordinate of the point of tangency....
so, y = -6(3) + 7
y = ????

Answer 10

(and that will not be the answer yet either...)

Answer 11

should give them the solution as you go so they know what they should be getting y=k - x^2

Answer 12

Did you find y = ???

Answer 13

y =-11

Answer 14

Ok...,
so plugging this into the first equation along with x=3, you have:
-11 = k -(3)^2

now do you know how k is obtained?

Answer 15

ohh okay yes thank you!

Answer 16

you're welcome