Question

Find the values of m for which the line with equation y=mx+2 does not intersect the parabola with equation y=(x-1)^2 + 5.

I am not sure how to solve this problem. I know that both equations equal each other when it intersects but what happens if they don't intersect. Please help me.

Answer 1

if the line intersects, then we have

(x-1)^2+5 = mx+2
x^2-2x+6 = mx+2
x^2-(m+2)x+4 = 0

For no solutions, you must have the discriminant negative:

(m+2)^2 - 16 < 0

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