SOLUTION: For what value of b will the line y=-2x+b be tangent to the parabola y=3x^2+4x-1 a method requiring the quadratic formula and substitution is required

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: For what value of b will the line y=-2x+b be tangent to the parabola y=3x^2+4x-1 a method requiring the quadratic formula and substitution is required       Log On


   

Question 315287: For what value of b will the line y=-2x+b be tangent to the parabola y=3x^2+4x-1
a method requiring the quadratic formula and substitution is required
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Well that's certainly not the easy way.
You have two equations.
y=3x%5E2%2B4x-1
y=-2x%2Bb
Look for the intersection point.
Set them equal to each other.
3x%5E2%2B4x-1=-2x%2Bb
3x%5E2%2B6x-%281%2Bb%29=0
Since the line is a tangent point, the curves only intersect at one point.
Then x must be a double root and the equation must be a perfect square.
Complete the square to solve for both x and b.
3%28x%5E2%2B2x%29-%281%2Bb%29=0
3%28x%5E2%2B2x%2B1%29-%281%2Bb%29=3
3%28x%2B1%29%5E2=1%2Bb%2B3
3%28x%2B1%29%5E2=b%2B4=0
The x coordinate for intersection is x=-1
and also b=-4
highlight%28y=-2x-4%29