Answer:
[tex]f(x)=(x-4.5)^{2}-6.25[/tex] or [tex]f(x)=(1/4)(2x-9)^{2}-6.25[/tex]
Step-by-step explanation:
we have
[tex]f(x)=x^{2}-9x+14[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]f(x)-14=x^{2}-9x[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]f(x)-14+4.5^{2}=x^{2}-9x+4.5^{2}[/tex]
[tex]f(x)+6.25=x^{2}-9x+4.5^{2}[/tex]
Rewrite as perfect squares
[tex]f(x)+6.25=(x-4.5)^{2}[/tex]
[tex]f(x)=(x-4.5)^{2}-6.25[/tex]
[tex]f(x)=(1/4)(2x-9)^{2}-6.25[/tex]
