Question

Rewrite the function by completing the square. f(x)= x^{2} -9 x +14f(x)=x 2 −9x+14

Answer 1

Answer:

$f(x)=(x-4.5)^{2}-6.25$  or $f(x)=(1/4)(2x-9)^{2}-6.25$

Step-by-step explanation:

we have

$f(x)=x^{2}-9x+14$

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

$f(x)-14=x^{2}-9x$

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

$f(x)-14+4.5^{2}=x^{2}-9x+4.5^{2}$

$f(x)+6.25=x^{2}-9x+4.5^{2}$

Rewrite as perfect squares

$f(x)+6.25=(x-4.5)^{2}$

$f(x)=(x-4.5)^{2}-6.25$

$f(x)=(1/4)(2x-9)^{2}-6.25$