what is the vertex of the graph of y = 3x² + 2x + 1?\n(-1/3,0)\n(-1/3,2/3)\n(1/3,2)\n(1/3,0)

Explanation:

Step1: Identify coefficients

For the quadratic function $y = ax^{2}+bx + c$, here $a = 3$, $b = 2$, $c = 1$.

Step2: Find x - coordinate of vertex

Use the formula $x=-\frac{b}{2a}$. Substitute $a = 3$ and $b = 2$ into it: $x=-\frac{2}{2\times3}=-\frac{1}{3}$.

Step3: Find y - coordinate of vertex

Substitute $x = -\frac{1}{3}$ into $y = 3x^{2}+2x + 1$. $y=3\times\left(-\frac{1}{3}\right)^{2}+2\times\left(-\frac{1}{3}\right)+1$. $y = 3\times\frac{1}{9}-\frac{2}{3}+1$. $y=\frac{1}{3}-\frac{2}{3}+1$. $y=\frac{1 - 2+3}{3}=\frac{2}{3}$.

Answer:

B. $\left(-\frac{1}{3},\frac{2}{3}\right)$