Question

For the quadratic function f(x) = x2 + 6x +11:

a. Use the idea of completing the square to write it in graphing form.

Answer 1

Explanation:

Make f(x) = 0

`{x}^(2) + 6x + 11 = 0`

First, we move the constant term to the right hand side of the equality sign.

`{x}^(2) + 6x = - 11`

Then, we half the coefficient of x and square our result.

`( (6)/(2) ) ^(2) = 3 ^(2) = 9`

Now, we add the result to the both sides of the equation.

`{x}^(2) + 6x + 9 = - 11 + 9`

We can see that x²+6x+9 = (x+3)² {Try factorizing}

Therefore,

(x+3)²= -2

(x+3)²+2= 0

f(x)= (x+3)²+2

Which is the f(x) in graphing form.