C9 - translate between different forms of quadratic equations
Originator: Ian and Sam
Explanation:
From Transformational to general form
To convert your quadratic equation from Transformational to General form, you first expand the (x-h)^2. then you would multiply the x side of the equation by (a). Then you would move k to the other side of the equation. you will be left with y equaing an x^2 an x and a interger.
From Transformational to Function form
To convert your quadratic equation from Transformational to Function form, you multiply the x side of the equation by a, then you move k to the other side of the equation. you will be left with
y=a(x-h)^2 +k.
From General to Transformational form
to convert your quadratic equation from General to Transformational, you move your intergers to the y side of the equation, if there is an a infront of the x^2 factor it out from the right side of the equation. now you need to add a number to each side to complete the square. For the side with the x's you take half your b term and take it to the power of 2. you add this number inside the brackets, you add what ever the interget inside the brackets times the a value to give you the number to add to the y side. now you factor the trinomial to get y-k=a(x-h)^2. From here you will multiply both sides of the equation by the recrical of a, to move a to the y side of the equation.
From General to Function form
To convert your quadratic equation from General to function form, you follow the same steps used for converting General to Transformational, however once you get to y-k=a(x-h)^2 you just move k to the x side of the equation to give you your function form of y=a(x-h)^2 +k.
From Function to General form
To convert your quadratic equation from function form to general form, you expand the (x-h)^2 so that you get y=a( x^2 -2hx + h^2) +k, from here you multiply the brackets by your a term, finially add your ah^2 and k values, so you are left with your y=ax^2+bx+c.
From Function to Transformational form
To convert your quadratic equation from function form to Transformational form, you move the k term to the y side of the equation. From here multiply both sides of the equation by the reciprical of a, so you end up with
1/a (y-k) = (x-h)^2
sample problem: Change the equation provided
1/2 (y-3)= (x-4)2 to general and function form. change the equation y = 2x2 - 16x +35 to transformational and function form, change the equation
y = 2(x-4) 2 + 3 to general form and transformational form.
Solution:
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Transformational to General
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1/2 (y-3)= (x-4)2
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1/2 (y-3)= x2 –8x + 16
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y-3 = 2x2 – 16x + 32
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y = 2x2 – 16x + 32+3
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y = 2x2 – 16x +35
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Transformational to Function
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1/2 (y-3)= (x-4)2
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y-3 = 2 (x-4) 2
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y = 2(x-4) 2 + 3
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General to Transformational
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y = 2x2 - 16x +35
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y – 35 = 2x2 - 16x
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y –3= 2(x2 - 8x +16)
* (+ 32 to each side [(b/2)2])
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y –3= 2(x-4)2
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1/2(y –3)= (x-4)2
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General to Function
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y = 2x2 - 16x +35
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y – 35 = 2x2 - 16x
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y –3= 2(x2 - 8x +16)
* (+ 32 to each side [(b/2)2])
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y –3= 2(x-4)2
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y = 2(x-4) 2 + 3
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Function to General
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y = 2(x-4) 2 + 3
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y = 2(x2 –8x + 16) + 3
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y = 2x2 – 16x + 32+3
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y = 2x2 – 16x +35
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Function to Transformational
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y = 2(x-4) 2 + 3
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y-3 = 2 (x-4) 2
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1/2 (y-3)= (x-4)2
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Comments (1)
Anonymous said
at 8:09 pm on Mar 13, 2007
Ian and Sam, nice work on you outcome.
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