How do you write the quadratic function #y=x^2+12x+6# in vertex form?

Answer 1

#y=(x+6)^2-30#

#"the equation of a parabola in "color(blue)"vertex form"# is.
#color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))# where ( h , k ) are the coordinates of the vertex and a is a constant.
#"for a quadratic in standard form " ax^2+bx+c#
#x_(color(red)"vertex")=-b/(2a)#
#x^2+12x+6" is in this form"#
#"with " a=1,b=12,c=6#
#rArrx_(color(red)"vertex")=-12/2=-6#
#"substitute this value into the equation for y"#
#y_(color(red)"vertex")=(-6)^2+(12xx-6)+6=-30#
#rArrcolor(magenta)"vertex "=(-6,-30)#
#rArry=(x+6)^2-30larrcolor(red)" in vertex form"#
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Answer 2

To write the quadratic function ( y = x^2 + 12x + 6 ) in vertex form, you complete the square. This involves rearranging the equation to express it as ( y = a(x - h)^2 + k ), where ((h, k)) represents the vertex of the parabola.

First, factor out the coefficient of (x^2) from the first two terms: [ y = 1(x^2 + 12x) + 6 ]

Next, complete the square inside the parentheses by adding and subtracting ((12/2)^2 = 36): [ y = 1(x^2 + 12x + 36 - 36) + 6 ]

Now, rewrite the expression as a perfect square trinomial and factor the constant term out of the parentheses: [ y = (x + 6)^2 - 36 + 6 ]

Combine like terms: [ y = (x + 6)^2 - 30 ]

So, the quadratic function ( y = x^2 + 12x + 6 ) in vertex form is ( y = (x + 6)^2 - 30 ).

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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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