For the quadratic function f(x) = x2 + 6x +11:
a. Use the idea of completing the square to write it in graphing form.

Respuesta :

Step-by-step explanation:

Make f(x) = 0

[tex] {x}^{2} + 6x + 11 = 0[/tex]

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

[tex] {x}^{2} + 6x = - 11[/tex]

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

[tex]( \frac{6}{2} ) ^{2} = 3 ^{2} = 9[/tex]

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

[tex] {x}^{2} + 6x + 9 = - 11 + 9[/tex]

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.

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