Question

Rewrite the quadratic function in standard form.f(x) = 3x2 − 4xf(x) = Give the vertex.(x, y) =

Answer 1

`\begin{gathered} f(x)=3(x-(2)/(3))^2-(4)/(3) \\ vertex=((2)/(3),-(4)/(3)) \end{gathered}`

Explanations:

Given the quadratic equation expressed as:

`f(x)=3x^2-4x`

Factor out 3 from the expression

`f(x)=3(x^2-(4)/(3)x)`

Complete the square of the expression in bracket

`\begin{gathered} f(x)=3(x^2-(4)/(3)x+((1)/(2)\cdot(4)/(3))^2-((1)/(2)\cdot(4)/(3))^2) \\ f(x)=3(x^2-(4)/(3)x+((2)/(3))^2-((2)/(3))^2) \\ f(x)=3(x^2-(4)/(3)x+((2)/(3))^2-(4)/(9)) \\ f(x)=3(x-(2)/(3))^2-3((4)/(9)) \\ f(x)=3(x-(2)/(3))^2-(4)/(3) \\ \end{gathered}`

Since the vertex form of a quadratic equation is in the form f(x) = a(x-h)^2+k where (h, k) is the vertex.The vertex of the resulting function is (2/3, -4/3)