Question

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

Explanation:

Step1: Use discriminant for 1 x-intercept

A quadratic $y=ax^2+bx+c$ has exactly one x-intercept when its discriminant $\Delta = b^2 - 4ac = 0$.

Step2: Identify coefficients

Here, $a=18$, $b=m$, $c=2$. Substitute into discriminant:
$$m^2 - 4(18)(2) = 0$$

Step3: Simplify and solve for $m$

Calculate $4(18)(2)=144$, so:
$$m^2 = 144$$
Take square roots:
$$m = \pm 12$$
From the options, $12$ is provided.

Answer:

12