Parabola

Well paralle lines have common slopes..

Then the line you want will share the slope with y - 3x = 4
so since y = mx + c
then y = 3x + 4
then m = 3

the turning point of the parabola will be where dy/dx is 0...
so when y = -x^2 + 2x + 5
dy/dx = -2x + 2 = 0 (at a turning point)
2x = 2
x = 1
so y = -(1)^2 + 2(1) + 5
y = 6
(1 , 6) is the point where it turns

so y - y' = m(x - x')
y - 6 = 3(x - 1)
y - 6 = 3x - 3
therefore 3x - y + 3 = 0

ok
Great work.

You said:

"therefore 3x - y + 3 = 0"

Book's answer is y = 3x + 3.

Let's see:

3x - y + 3 = 0

-y = -3x - 3

DIVIDE BOTH SIDES by -1.

y = 3x + 3.

Got it.

Thanks

welcome again