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 \\eq 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) = (-b)/(2a);`

`y_(0) = ax_(0)^(2) + bx_(0) + c ~ \mathrm{or} ~ y_(0) = -(b^(2) - 4ac)/(4a).`

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

`x_(0) = (-(-12))/(2 \cdot 3) = (12)/(6) = 2;`

`y_(0) = 3 \cdot 2^(2) - 12 \cdot 2 + 7 = -5.`

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