Rewrite the function by completing the square. f (x) = x2-9x+14f (x) = x^{2} - 9 x + 14 f (x) = x 2 - 9x+14 f, left parenthesis, x, right parenthesis, equals, x, squared, minus, 9, x, plus, 14 f (x) = f (x) = f (x) = f, left parenthesis, x, right parenthesis, equals (x + (x + (x + left parenthesis, x, plus) 2+) ^2+) 2 + right parenthesis, squared, plus

x² - 9x + 14 by completing the square is (x - 9/2) ² - 25/4

Step-by-step explanation:

Given x² - 9x + 14

To rewrite by completing the square, we need to write this in the form (a + b) ² or (a - b) ² without changing the value of the expression.

(a + b) ² = a² + 2ab + b² (equation 1)

(a - b) ² = a² - 2ab + b² (equation 2)

x² - 9x + 14 = x² - 2 (x) (9/2) + (9/2) ² - 25/4 (equation 3)

Comparing (equation 3) with (equation 1) and (equation 2), we can see that it takes the form of (equation 1), though, surplus of 25/4, where a = x, and b = 9/2.

So

x² - 2 (x) (9/2) + (9/2) ² = x² - 2 (x) (9/2) + 81/4 = (x - 9/2) ²

Which means

x² - 9x + 14

= x² - 2 (x) (9/2) + 81/4 - 25/4

= x² - 2 (x) (9/2) + (9/2) ² - 25/4

= (x - 9/2) ² - 25/4

And the square is completed.