SOLUTION: Given the quadratic function y=x^2-x+k-1 and the linear function y=x+1, find the number of points that their graphs have in common. (assume k>4)
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-> SOLUTION: Given the quadratic function y=x^2-x+k-1 and the linear function y=x+1, find the number of points that their graphs have in common. (assume k>4)
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Question 1014924: Given the quadratic function y=x^2-x+k-1 and the linear function y=x+1, find the number of points that their graphs have in common. (assume k>4) Answer by robertb(5830) (Show Source):
You can put this solution on YOUR website! Solve the system of equations and y = x + 1.
Then , or .
The discriminant is then equal to .
Since it is given that k > 4, it follows that:
-4k < -16,
12 - 4k < 12 - 16 = -4,
12 - 4k < -4 < 0,
hence the discriminant is negative, and thus the system has no (real) solutions. Therefore the two graphs don't have points in common. (They do not intersect.)
