How do you write #f(x) = x^2 - 4x - 10# in vertex form?

Answer 1

#f(x)=(x-2)^2-14#

#"the equation of a parabola in "color(blue)"vertex form"# is.
#color(red)(bar(ul(|color(white)(2/2)color(black)(f(x)=a(x-h)^2+k)color(white)(2/2)|)))#
#"where "(h,k)" are the coordinates of the vertex and a is "# #"a multiplier"#
#"to obtain this form "color(blue)"complete the square"#
#• " the coefficient of the "x^2" term must be 1 which it is"#
#• " add/subtract "(1/2"coefficient of the x-term")^2" to"# #x^2-4x#
#rArrf(x)=x^2+2(-2)xcolor(red)(+4)color(red)(-4)-10#
#color(white)(rArrf(x))=(x-2)^2-14larrcolor(red)"in vertex form"#
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Answer 2

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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Answer from HIX Tutor

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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