# How do you write #f(x)=2x^2+12x+12# in vertex form?

Vertex form is also known as completing the square

Write as:

When we start to change things the equation becomes untrue. So we need to introduce the correction

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Move the power of 2 from

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Halve the 6 from

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Remove the

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Determine the value of

If you were to square the bracket we would have

So we write:

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Substitute this into equation(1)

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To write the quadratic function (f(x) = 2x^2 + 12x + 12) in vertex form, follow these steps:

- Factor out the leading coefficient (2) from the terms involving (x^2) and (x):

[f(x) = 2(x^2 + 6x) + 12]

- Complete the square inside the parentheses by adding and subtracting the square of half the coefficient of (x), which is ((6/2)^2 = 9):

[f(x) = 2(x^2 + 6x + 9 - 9) + 12]

- Rewrite the expression inside the parentheses as a perfect square trinomial:

[f(x) = 2[(x + 3)^2 - 9] + 12]

- Distribute (2) and simplify:

[f(x) = 2(x + 3)^2 - 18 + 12]

- Combine the constant terms:

[f(x) = 2(x + 3)^2 - 6]

So, the vertex form of (f(x) = 2x^2 + 12x + 12) is (f(x) = 2(x + 3)^2 - 6).

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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.

- Given #f(x) = x^4+ax^3+bx^2+cx+d# with #f(1) = 1#, #f(2) = 5#, #f(3) = 19# and #f(6) = 665#, what is the value of #f(4)+f(5)# ?
- How do you solve #y=5x^2+20x+23# using the completing square method?
- How do you solve #3x² + 7x = -2#?
- What is the vertex of the parabola #y = -2(x+1)^2 +7#?
- What is the vertex of #y=2(x +3)^2 -8x #?

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