Find the vertex of the parabola.
-$$g ( x ) = x ^ { 2 } - 13 x + 6$$
A) $\left( \frac { 13 } { 2 } , - \frac { 145 } { 4 } \right)$
B) $\left( \frac { 13 } { 2 } , \frac { 531 } { 4 } \right)$
C) $\left( \frac { 13 } { 4 } , \frac { 163 } { 8 } \right)$
D) $\left( - \frac { 13 } { 2 } , \frac { 531 } { 4 } \right)$

Question

Quizplus · Accepted Answer

The vertex of a parabola in the form $f(x) = ax^2 + bx + c$ can be found using the formula $\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)$. For $g(x) = x^2 - 13x + 6$, $a = 1$, $b = -13$, and $c = 6$. Thus, the x-coordinate of the vertex is $-\frac{-13}{2(1)} = \frac{13}{2}$. Substituting $\frac{13}{2}$ into $g(x)$ gives the y-coordinate: $g\left(\frac{13}{2}\right) = \left(\frac{13}{2}\right)^2 - 13\left(\frac{13}{2}\right) + 6 = -\frac{145}{4}$. Therefore, the vertex is $\left(\frac{13}{2}, -\frac{145}{4}\right)$.

Find the Vertex of the Parabola g(x)=x2−13x+6g ( x ) = x ^ { 2 } - 13 x + 6g(x)=x2−13x+6

Find the Vertex of the Parabola $g ( x ) = x ^ { 2 } - 13 x + 6$