SOLUTION: Find m, (m < 0), such that y = mx -7 has one intersection point with y = -m(x +1)² -5

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Question 1063748: Find m, (m < 0), such that y = mx -7 has one intersection point with y = -m(x +1)² -5
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39629) About Me  (Show Source):
You can put this solution on YOUR website!
mx-7=-m%28x%2B1%29%5E2-5 must have exactly ONE solution.

mx-7=-m%28x%5E2%2B2x%2B1%29-5
mx-7=-mx%5E2-2mx-m-5
-mx%2B7=mx%5E2%2B2mx%2Bm%2B5
mx%5E2%2B3mx%2Bm%2B5-7=0
highlight_green%28mx%5E2%2B3mx%2Bm-2=0%29

You want the discriminant to be equal to 0, to make sure the mx-7=-m%28x%2B1%29%5E2-5 has just one solution and the original two equations intersect in just one point.

Using the discriminant of the equation outlined in green,
%283m%29%5E2-4%2Am%2A%28m-2%29=0
Solve this for m.

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

Find m, (m < 0), such that y = mx -7 has one intersection point with y = -m(x +1)² -5
highlight_green%28m+=+-+8%2F5%29