SOLUTION: For what value of b will the line y=-2x+b be tangent to the parabola y=3x^2+4x-1

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: For what value of b will the line y=-2x+b be tangent to the parabola y=3x^2+4x-1      Log On


   

Question 315279: For what value of b will the line y=-2x+b be tangent to the parabola y=3x^2+4x-1
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The slope of the tangent of the parabola is equal to the value of the derivative.
y=3x%5E2%2B4x%2B1
dy%2Fdx=6x%2B4=-2
6x%2B4=-2
6x=-6
x=-1
So at the point x=-1, the slope of the tangent line equals -2.
At that point,
y=3x%5E2%2B4x%2B1=3-4-1=-2
So then
y=-2x%2Bb
-2=-2%28-1%29%2Bb
b=-4
and the equation of the tangent line is,
y=-2x-4
.
.
.