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 $ax^{2}+bx + c = 0$, the discriminant $\Delta=b^{2}-4ac$. When $\Delta = 0$, the quadratic - function has exactly one $x$ - intercept. The given quadratic function is $y = 18x^{2}+mx + 2$, which can be written as the quadratic equation $18x^{2}+mx + 2=0$, where $a = 18$, $b = m$, and $c = 2$.

Step2: Set the discriminant equal to 0

We set $\Delta=m^{2}-4\times18\times2=0$. So, $m^{2}-144 = 0$.

Step3: Solve for m

Add 144 to both sides of the equation: $m^{2}=144$. Take the square - root of both sides: $m=\pm12$.

Answer:

C. 12