Question

Find the values of a and b such that
x^2-4x+9=(x+a)^2+b

Answer 1

a = -2

b = 5

Explanation:

We can identify the right side of the equation as completing the square. So, we simply complete the square for x² - 4x + 9 to find our answer,

Step 1: Isolate xs

x² - 4x = -9

Step 2: Complete the square

x² - 4x + 4 = -9 + 4

(x - 2)² = -5

Step 3: Move -5 over

(x - 2)² + 5

And we have our answer!