How do you write #f(x) = x^2 - 4x - 10# in vertex form?
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To write the quadratic function ( f(x) = x^2 - 4x - 10 ) in vertex form, complete the square.
First, factor out any common factors from the terms involving ( x ), which in this case, is 1. Then, complete the square by halving the coefficient of ( x ) (which is -4), squaring it, and adding it inside the parentheses. This will ensure that the quadratic expression is a perfect square trinomial.
The vertex form of the quadratic function is ( f(x) = (x - h)^2 + k ), where ( (h, k) ) is the vertex of the parabola. To find ( h ) and ( k ), use the formula ( h = -\frac{b}{2a} ) and evaluate ( f(h) ) to find ( k ).
Given the quadratic function ( f(x) = x^2 - 4x - 10 ), ( a = 1 ), ( b = -4 ), and ( c = -10 ).
[ h = -\frac{b}{2a} = -\frac{-4}{2(1)} = 2 ]
[ k = f(2) = (2)^2 - 4(2) - 10 = -14 ]
So, the vertex form of the quadratic function is ( f(x) = (x - 2)^2 - 14 ).
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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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