Question

Rewrite the function by completing the square.
f(x) = x2 – 10x + 44
+
f(x) = (x+

Answer 1

`f(x)=(x-5)^(2)+19`

Explanation:

we have

`f(x)=x^(2)-10x+44`

Group terms that contain the same variable, and move the constant to the opposite side of the equation

`f(x)-44=x^(2)-10x`

Complete the square. Remember to balance the equation by adding the same constants to each side.

`f(x)-44+25=x^(2)-10x+25`

`f(x)-19=x^(2)-10x+25`

Rewrite as perfect squares

`f(x)-19=(x-5)^(2)`

`f(x)=(x-5)^(2)+19`