SOLUTION: Find the value(s) of M that make the equation: 3-Mx+x^2 tangent to the x-axis. Show your work. Draw the function.

Question 873184: Find the value(s) of M that make the equation: 3-Mx+x^2 tangent to the x-axis. Show your work. Draw the function.
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Complete the Square for and expect vertex to have y=0.

, using to complete the square.

This shows vertex to be and
That is what must be zero: the y value. Solve for M in ;

or
-
-
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FINDING THE POSSIBLE VERTEX INCLUDING x:
The corresponding x values and ordered pair vertices are then
(-sqrt(3), 0)
OR
(sqrt(3), 0)
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Finishing this using the negative valued vertex to demonstrate,

You can carry through similar steps to use the positive-valued vertex if you want.

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