SOLUTION: For what value of k does the following system have exactly one solution? y=x^2 y=x+k

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Question 1150724: For what value of k does the following system have exactly one solution?
y=x^2
y=x+k
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


y+=+x%5E2
y+=+x%2Bk

x%5E2+=+x%2Bk
x%5E2-x-k+=+0

The system has one solution when the quadratic has a single root.

A quadratic has a single root when the discriminant is 0:

b%5E2-4ac+=+0
%28-1%29%5E2-4%281%29%28-k%29+=+0
1%2B4k+=+0
k+=+-1%2F4

ANSWER: k = -1/4

A graph (window (-1,1) by (-1,1)....) x^2 (red); x-1/4 (green)

graph%28400%2C400%2C-1%2C1%2C-1%2C1%2Cx%5E2%2Cx-.25%29