for which value of m does the graph of y = 18x² + mx + 2 have exactly one x - intercept?\n0\n9\n12\n16

Explanation:

Step1: Recall the discriminant formula

For a quadratic equation $ax^{2}+bx + c = 0$ (here $y=18x^{2}+mx + 2$ so $a = 18$, $b=m$, $c = 2$), the discriminant $\Delta=b^{2}-4ac$. When the graph has exactly one $x$-intercept, $\Delta = 0$.

Step2: Set up the equation

Set $\Delta=0$, so $m^{2}-4\times18\times2=0$.

Step3: Simplify the equation

$m^{2}-144 = 0$.

Step4: Solve for $m$

$m^{2}=144$, then $m=\pm12$. Among the given options, the correct value is $12$.

Answer:

C. 12