To get the graph to have one x-intercept, we must find the m value where the discriminant of the equation will equal 0.
The discriminant for a graph with one x-intercept is found with the following formula:
[tex]b^2 - 4ac = 0[/tex]
Plug in the values of the equation into this formula:
[tex]\text{a = 18, b = m, c = 2}[/tex]
[tex]m^2 - 4(18)(2) = 0[/tex]
[tex]m^2 - 144 = 0[/tex]
Add 144 to both sides:
[tex]m^2 = 144[/tex]
Square root both sides to get m by itself:
[tex]\sqrt{144} = \pm 12[/tex]
[tex]m = 12, \ m = -12[/tex]
In order for the graph to have one x-intercept, m must equal -12 or 12.
