# How do you write #f(x)= -3x^2 +12x -11# in vertex form?

y = -3(x - 2)^2 + 1

x-coordinate of vertex: x = -b/(2a) = -12/-6 = 2 y-coordintae of vertex: y(2) = -12 + 24 - 11 = 1 Vertex form: y = -3(x - 2)^2 + 1 Check. Develop y to get back to standard form: y = -3(x^2 - 4x + 4) + 1 = -3x^2 + 12x - 11. OK

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To write the function ( f(x) = -3x^2 + 12x - 11 ) in vertex form, follow these steps:

- Factor out the coefficient of ( x^2 ) from the first two terms: ( -3(x^2 - 4x) - 11 ).
- Complete the square inside the parentheses by adding and subtracting ((\frac{4}{2})^2 = 4): ( -3(x^2 - 4x + 4 - 4) - 11 ).
- Rewrite the expression inside the parentheses as a perfect square: ( -3((x - 2)^2 - 4) - 11 ).
- Distribute the ( -3 ) and simplify: ( -3(x - 2)^2 + 12 - 11 ).
- Combine like terms: ( -3(x - 2)^2 + 1 ).

So, the function ( f(x) = -3x^2 + 12x - 11 ) in vertex form is ( f(x) = -3(x - 2)^2 + 1 ).

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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.

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