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

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

1 Answer

9 votes

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 +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.

User Gazmir
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