# How do you write #f(x)= -2x^2+20x-49# in vertex form?

So, we have:

Once solved, you're x value of your vertex is 5. Now, you plug 5 into your original standard form equation.

Finally, your vertex is:

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To write ( f(x) = -2x^2 + 20x - 49 ) in vertex form, complete the square. The vertex form of a quadratic function is ( f(x) = a(x - h)^2 + k ), where ( (h, k) ) is the vertex of the parabola.

First, factor out the common factor ( -2 ) from the quadratic terms: [ f(x) = -2(x^2 - 10x) - 49 ]

Complete the square inside the parentheses: [ f(x) = -2(x^2 - 10x + 25 - 25) - 49 ]

Simplify inside the parentheses and distribute: [ f(x) = -2[(x - 5)^2 - 25] - 49 ]

Apply the distributive property: [ f(x) = -2(x - 5)^2 + 50 - 49 ]

Combine like terms: [ f(x) = -2(x - 5)^2 + 1 ]

So, the vertex form of the function ( f(x) = -2x^2 + 20x - 49 ) is ( f(x) = -2(x - 5)^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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