Question

The equation f(x) = 3x2 − 24x + 8 represents a parabola. What is the vertex of the parabola?

Answer 1

$\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{3}x^2\stackrel{\stackrel{b}{\downarrow }}{-24}x\stackrel{\stackrel{c}{\downarrow }}{+8} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{-24}{2(3)}~~,~~8-\cfrac{(-24)^2}{4(3)} \right)\implies (4~~,~~8-48)\implies (4~~,~-40)$