SOLUTION: show that the straight line y=mx+b is a tangent to the curve y=-x^2-3x+4 if and only if (m+3)^2=4(b-4) help would be much appreciated, thanks!

Question 1036785: show that the straight line y=mx+b is a tangent to the curve y=-x^2-3x+4 if and only if (m+3)^2=4(b-4)
help would be much appreciated, thanks!
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Your plan to show this is examine the difference between the the two expressions as functions, like the difference as SUBTRACTION between the two functions. The difference will be 0 for the tangency point. You will obviously have the couple of variables in your finished equation regardless of the form you use.

The two equations cannot be graphed until values of m and b are known, given, or picked. WAIT. Not completely true. You can graph the parabola but not the line. You must have values for m and b.
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