Question

Find the minimum value of the function

Answer 1

$\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\ \begin{array}{lccclll} g(x) = &{{ 2}}x^2&{{ +4}}x&{{ -5}}\\ &\uparrow &\uparrow &\uparrow \\ &a&b&c \end{array}\qquad \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right) \\\\\\ \left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad \stackrel{minimum}{-5-\cfrac{4^2}{4(2)}}\right)$