Question

Rewrite the function by completing the square. [g(x) = 2x² - 7x + 5]

Answer 1

To rewrite the function g(x) = 2x² - 7x + 5 by completing the square, follow these steps: simplify the expression inside the parentheses, add and subtract the square of the value obtained in step 1, add or subtract any additional terms, and simplify the remaining expression.

Step-by-step explanation:

To rewrite the function g(x) = 2x² - 7x + 5 by completing the square, we follow these steps:

1. First, we take the coefficient of the x² term, which is 2, and divide it by 2 to get 1.
2. We add and subtract the square of the value obtained in step 1, which is 1² = 1, inside the parentheses:
3. g(x) = 2(x² - 7/2x + 1) + 5 - 2(1)
4. Next, we simplify the expression inside the parentheses. To do this, we take half the coefficient of the x term, which is -7/2, square it, and add it both inside and outside the parentheses:
5. g(x) = 2(x² - 7/2x + 1) + 5 - 2(1)
6. g(x) = 2(x - 7/4)² + 5 - 2
7. Finally, we simplify the remaining expression:
8. g(x) = 2(x - 7/4)² + 3