Question

What value of m does the graph y = 18x2 + mx + 2 have exactly one x-intercept?

Answer 1

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.