Question

27 - 4x + x² can be written in the form (x + a)²+ b, where a and b are numbers. Work out the values of a and b.​

Answer 1

To rewrite the expression 27 - 4x + x² in the form (x + a)² + b, we can complete the square.

Starting with x² + (-4x) + 27:

x² - 4x + 4x² = 4x² - 4x

Adding (4/2)² = 4 to both sides:

4x² - 4x + 4 = 4x² - 4x + 4

The expression is now in the form (x - 2)² + 0, so a = -2 and b = 0.

Therefore, 27 - 4x + x² = (x - 2)² + 0.