Question

Find the vertex of a quadratic function written in standard form. f(x)=-3x^2+18x-27

Answer 1

`\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{\textit{\small a}}{\downarrow }}{-3}x^2\stackrel{\stackrel{\textit{\small b}}{\downarrow }}{+18}x\stackrel{\stackrel{\textit{\small c}}{\downarrow }}{-27} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)`

`\left(-\cfrac{ 18}{2(-3)}~~~~ ,~~~~ -27-\cfrac{ (18)^2}{4(-3)}\right) \implies\left( - \cfrac{ 18 }{ -6 }~~,~~-27 - \cfrac{ 324 }{ -12 } \right) \\\\\\ \left( \cfrac{ 18 }{ 6 }~~,~~-27 + \cfrac{ 324 }{ 12 } \right)\implies \left( \cfrac{ 18 }{ 6 }~~,~~-27 + 27 \right)\implies (~3~~,~~ 0~)`