Question

Find the vertex of Parabola $y=3x^2-7x+4$

Answer 1

The vertex is $\left(\frac{7}{6}, -\frac{1}{12}\right)$.

Answer 2

The x-coordinate of the vertex is given by $x_v = \frac{-b}{2a}$. For $y = 3x^2 - 7x + 4$, $a=3$ and $b=-7$. So, $x_v = \frac{-(-7)}{2(3)} = \frac{7}{6}$. Substituting $x_v$ into the equation: $y_v = 3\left(\frac{7}{6}\right)^2 - 7\left(\frac{7}{6}\right) + 4 = 3\left(\frac{49}{36}\right) - \frac{49}{6} + 4 = \frac{49}{12} - \frac{98}{12} + \frac{48}{12} = -\frac{1}{12}$. The vertex is $\left(\frac{7}{6}, -\frac{1}{12}\right)$.