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

Step-by-step 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.

$( \frac{6}{2} ) ^{2} = 3 ^{2} = 9$

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.