For which value of m does the graph of y = 18x² + mx + 2 have exactly one x-intercept?
0, 9, 12, 16

Solution:

Given: Equation of graph y = 18x² + mx + 2

Also it is given that the graph has only one intercept

We know that the graph will have two intercepts but if the determinant is 0 then the intercept will coincide. 

The discriminant will be b² - 4ac.

⇒ m² - 4(18)(2)

⇒ m² - 144

For intercept to coincide the determinant should be 0.

⇒ m² - 144 = 0

⇒ m² = 144

Applying square root on both sides

⇒ √m² = √144

⇒ m = ±12

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

Summary:

The graph y = 18x² + mx + 2 will have only one intercept when m = 12 or m = -12.