Question

What are the coordinates of the vertex for f(x) = x2 + 6x + 13

(4, 4)
(−4, 4)
(3, 4)
(−3, 4)

Answer 1

$\bf\textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{llccll} y = &{{ 1}}x^2&{{ +6}}x&{{ +13}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)$