Question

What is the vertex of g(x)=8x^2 - 48x + 65?

(-3,-7)
(3,-7)
(24, -7)
(-24, -7)

Answer 1

`\textit{vertex of a vertical parabola, using coefficients} \\\\ g(x)=\stackrel{\stackrel{\textit{\small a}}{\downarrow }}{8}x^2\stackrel{\stackrel{\textit{\small b}}{\downarrow }}{-48}x\stackrel{\stackrel{\textit{\small c}}{\downarrow }}{+65} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)`

`\left(-\cfrac{ -48}{2(8)}~~~~ ,~~~~ 65-\cfrac{ (-48)^2}{4(8)}\right) \implies\left( - \cfrac{ -48 }{ 16 }~~,~~65 - \cfrac{ 2304 }{ 32 } \right) \\\\\\ \left( \cfrac{ 48 }{ 16 }~~,~~65 - \cfrac{ 2304 }{ 32 } \right)\implies \left( \cfrac{ 48 }{ 16 }~~,~~65 - 72 \right)\implies (~3~~,~~ -7~)`