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.

Algebra ->  Graphs -> 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.      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
Complete the Square for y=x%5E2-Mx%2B3 and expect vertex to have y=0.

y=x%5E2-Mx%2B%28M%2F2%29%5E2%2B3-%28M%2F2%29%5E2, using %28M%2F2%29%5E2 to complete the square.
y=%28x-M%2F2%29%5E2%2B%283-%28M%2F2%29%5E2%29

This shows vertex to be x=M%2F2 and highlight_green%28y=3-%28M%2F2%29%5E2%29
That is what must be zero: the y value. Solve for M in 3-%28M%2F2%29%5E2=0;
%28M%2F2%29%5E2=3
M%5E2=3%2A4
M%5E2=3%2A2%2A2
M=-2sqrt%283%29 or M=2sqrt%283%29
-
-
--------------------------------------------------------------------
FINDING THE POSSIBLE VERTEX INCLUDING x:
The corresponding x values and ordered pair vertices are then
(-sqrt(3), 0)
OR
(sqrt(3), 0)
---------------------------------------------------------------------

Finishing this using the negative valued vertex to demonstrate,
y=%28x%2Bsqrt%283%29%29%5E2%2B3-%28M%2F2%29%5E2
y=%28x%2Bsqrt%283%29%29%5E2%2B3-%28-2sqrt%283%29%2F2%29%5E2
y=%28x%2Bsqrt%283%29%29%5E2%2B3-3
highlight%28y=%28x%2Bsqrt%283%29%29%5E2%29
You can carry through similar steps to use the positive-valued vertex if you want.

graph%28300%2C300%2C-7%2C4%2C-4%2C7%2C%28x%2Bsqrt%283%29%29%5E2%29