Question

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

Answer 1

12

Explanation:

plug it into desmos it works

Answer 2

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:


`√(144) = \pm 12`

`m = 12, \ m = -12`

In order for the graph to have one x-intercept, m must equal -12 or 12.