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:
\(b^2 - 4ac = 0\)
Plug in the values of the equation into this formula:
\(\text{a = 18, b = m, c = 2}\)
\(m^2 - 4(18)(2) = 0\)
\(m^2 - 144 = 0\)
Add 144 to both sides:
\(m^2 = 144\)
Square root both sides to get m by itself:
\(\sqrt{144} = \pm 12\)
\(m = 12, \ m = -12\)
In order for the graph to have one x-intercept, m must equal -12 or 12.
