# For which Value of m does the Graph of y = 18x^{2} + mx + 2 have Exactly One X-Intercept?

We will be using the concept of discriminant to solve this.

## Answer: The Graph of y = 18x^{2} + mx + 2 will have exactly one x-intercept if m = ±12.

Let's solve this step by step.

**Explanation:**

Given that, y = 18x^{2} + mx + 2

18x^{2} + mx + 2 = 0

Discriminant = m^{2} - 4 × 18 × 2 = m^{2} - 144

You can use Cuemath's Discriminant Calculator to find discriminants for any quadratic equation.

We will have exactly one x-intercept if the discriminant is equal to zero.

⇒ m^{2} - 144 = 0

m^{2} = 144

m = ±12

That is, for y = 18x^{2} − 12x + 2 and y = 18x^{2} + 12x + 2