Question

rewrite the function by completing the square f(x)=x^2-9x+14
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Answer 1

Answer:

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

Step-by-step explanation:

we have

f(x)=x^{2}-9x+14f(x)=x2−9x+14

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

f(x)-14=x^{2}-9xf(x)−14=x2−9x

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)−14+4.52=x2−9x+4.52

f(x)+6.25=x^{2}-9x+4.5^{2}f(x)+6.25=x2−9x+4.52

Rewrite as perfect squares

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

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

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