Determine the value of k in y = -0.5x^2 - kx + 2 that will result in the intersection of the line y = -3x + 4 with the quadratic at one point ?
1 Answer
Apr 13, 2018
Explanation:
We need the line to be tangent to the parabola. Since tangency is determined by the derivative, let's differentiate!
y' = -x - k
Since
-3 = -x - k
3 = x + k
Now we have
{(y = 4 -3x), (x+ k = 3), (y = -1/2x^2 - kx + 2):}
Substituting number three into number 1:
-1/2x^2 - kx + 2 = 4 - 3x
Now substitute
-1/2x^2 -(3 -x)x + 2 = 4 - 3x
-1/2x^2 -(3x- x^2) + 2 = 4 - 3x
-1/2x^2 - 3x + x^2 = 2 - 3x
1/2x^2 = 2
x^2 = 4
x = +-2
Therefore,
Hopefully this helps!