Question

Which of the following represents the result of completing the square for the function: g(x) = x^2 + 8x – 30?

Your answer:
a g(x) = (x + 4)^2 – 30
b g(x) = (x + 4)^2 - 46
c g(x) = (x + 8)^2 – 30
d g(x) = (x + 8)^2 – 94

Answer 1

To complete the square for the given function, add and subtract (-16) from the equation and simplify to obtain the result (x + 4)² - 46. Hence, b) is correct.

Step-by-step explanation:

To complete the square for the function g(x) = x² + 8x – 30, follow these steps:

1. Ensure that the coefficient of x² is 1. In this case, it already is, so no adjustment is needed.
2. Take half of the coefficient of x (in this case, half of 8 is 4) and square it to get the constant term that will be added and subtracted from the equation.
3. Write the equation as g(x) = (x + 4)² - 16 - 30.
4. Simplify the equation to get g(x) = (x + 4)² - 46.

Therefore, option (b) represents the result of completing the square for the function: g(x) = x² + 8x – 30.