What does the equation y 4x2 - 24x 42 become after completing the square?

Answer 1

To complete the square for the equation ( y = 4x^2 - 24x + 42 ), first factor out the 4 from the quadratic terms: ( y = 4(x^2 - 6x) + 42 ). Next, complete the square inside the parentheses by adding and subtracting ( 9 ) (which is ((\frac{6}{2})^2)): ( y = 4(x^2 - 6x + 9 - 9) + 42 ). This simplifies to ( y = 4((x - 3)^2 - 9) + 42 ), which further simplifies to ( y = 4(x - 3)^2 - 36 + 42 ), resulting in ( y = 4(x - 3)^2 + 6 ).