How do you write #f(x) = 4x^2  16x + 3# in vertex form?
where ( h , k ) are the coordinates of the vertex and a is a constant.
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To write the function ( f(x) = 4x^2  16x + 3 ) in vertex form, follow these steps:

Complete the square for the quadratic term ( 4x^2  16x ) by factoring out the coefficient of ( x^2 ) and halving the coefficient of ( x ) before squaring it.

Add and subtract the square of half the coefficient of ( x ) inside the parentheses to maintain the equivalence of the expression.

Rewrite the expression to isolate the squared term and simplify.

The resulting expression will be in the form ( f(x) = a(x  h)^2 + k ), where ( (h, k) ) represents the vertex of the parabola.
Applying these steps to the function ( f(x) = 4x^2  16x + 3 ):

Complete the square for the quadratic term ( 4x^2  16x ): [ 4x^2  16x = 4(x^2 + 4x) ]

Halve the coefficient of ( x ) and square it: [ (4x^2  16x) = 4(x^2 + 4x + 4  4) ]

Rewrite the expression to isolate the squared term and simplify: [ 4(x^2 + 4x + 4  4) = 4((x + 2)^2  4) ]

Expand and simplify: [ 4((x + 2)^2  4) = 4(x + 2)^2 + 16 ]
Thus, the function ( f(x) = 4x^2  16x + 3 ) in vertex form is ( f(x) = 4(x + 2)^2 + 16 ).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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