Rewrite the quadratic function in standard form by completing the square.
-$$f ( x ) = 3 x ^ { 2 } - 4 x$$
A) $f ( x ) = 3 \left( x - \frac { 2 } { 3 } \right) ^ { 2 } - \frac { 4 } { 3 }$
B) $f ( x ) = 3 \left( x - \frac { 2 } { 3 } \right) ^ { 2 } + \frac { 4 } { 9 }$
C) $f ( x ) = 3 \left( x + \frac { 4 } { 3 } \right) ^ { 2 } + \frac { 16 } { 9 }$
D) $f ( x ) = 3 \left( x + \frac { 4 } { 3 } \right) ^ { 2 } - \frac { 16 } { 9 }$

Question

Quizplus · Accepted Answer

To complete the square, factor out the coefficient of $x^2$ (which is 3) from the first two terms: $3(x^2 - \frac{4}{3}x)$. To complete the square inside the parentheses, add and subtract $(\frac{-4}{6})^2 = (\frac{-2}{3})^2 = \frac{4}{9}$ inside the parentheses, but since we factored out a 3, we need to adjust outside the parentheses by subtracting $3 \times \frac{4}{9} = \frac{4}{3}$. This gives $3(x - \frac{2}{3})^2 - \frac{4}{3}$.

Rewrite the Quadratic Function in Standard Form by Completing the Square