How do you write the quadratic function #y=x^2+12x+6# in vertex form?
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To write the quadratic function ( y = x^2 + 12x + 6 ) in vertex form, you complete the square. This involves rearranging the equation to express it as ( y = a(x - h)^2 + k ), where ((h, k)) represents the vertex of the parabola.
First, factor out the coefficient of (x^2) from the first two terms: [ y = 1(x^2 + 12x) + 6 ]
Next, complete the square inside the parentheses by adding and subtracting ((12/2)^2 = 36): [ y = 1(x^2 + 12x + 36 - 36) + 6 ]
Now, rewrite the expression as a perfect square trinomial and factor the constant term out of the parentheses: [ y = (x + 6)^2 - 36 + 6 ]
Combine like terms: [ y = (x + 6)^2 - 30 ]
So, the quadratic function ( y = x^2 + 12x + 6 ) in vertex form is ( y = (x + 6)^2 - 30 ).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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