Question

What is the vertex of g(x) = 3x2 − 12x + 7?

Answer 1

$\mathbf{Task.} ~ \mathrm{What~is~the~vertex~of}~ g(x) = 3x^{2} - 12x + 7?$

$\mathrm{Function~of~the~form} ~ f(x) = ax^{2} + bx + c, ~ a \neq 0, ~ \mathrm{is~ called~a~quadratic~function.}\\\mathrm{The~top} ~ (x_{0}; \ y_{0}) ~ \mathrm{of~this~function~can~be~found~by~the~formulas \colon}$

$x_{0} = \dfrac{-b}{2a};$

$y_{0} = ax_{0}^{2} + bx_{0} + c ~ \mathrm{or} ~ y_{0} = -\dfrac{b^{2} - 4ac}{4a}.$

$\mathrm{So,~for~the~function} ~ g(x) = 3x^{2} - 12x + 7 ~ \mathrm{we~have \colon}$

$x_{0} = \dfrac{-(-12)}{2 \cdot 3} = \dfrac{12}{6} = 2;$

$y_{0} = 3 \cdot 2^{2} - 12 \cdot 2 + 7 = -5.$

$Answer \colon (2; \ -5) \ \blacktriangle$