SOLUTION: How to convert an equation in standard form to factored form ? This equation in standard form is y=-2x^2+12x-4 in vertex form, it's y= -2(x-3)^2+14 So how to write it in facto

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: How to convert an equation in standard form to factored form ? This equation in standard form is y=-2x^2+12x-4 in vertex form, it's y= -2(x-3)^2+14 So how to write it in facto      Log On


   

Question 815213: How to convert an equation in standard form to factored form ?
This equation in standard form is y=-2x^2+12x-4
in vertex form, it's y= -2(x-3)^2+14
So how to write it in factored form /?
Thanks for any help.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The actual naming is reversed.
Standard Form is y=-2%28x-3%29%5E2%2B14 and General Form is y=-2x%5E2%2B12x-4.

You complete the square on general form to convert to standard form. Factor the -2 from the right side expression first:
y=-2%28x%5E2-6x%2B2%29
The term to add and subtract inside the trinomial factor is %28-6%2F2%29%5E2=9.
y=-2%28x%5E2-6x%2B9+-9%2B2%29
y=-2%28%28x-3%29%5E2-9%2B2%29
y=-2%28%28x-3%29%5E2-7%29
Now multiply using distributive property:
highlight%28y=-2%28x-3%29%5E2-14%29 now in standard form from which you can directly read the vertex point, (3,-14).


FACTORING THE EQUATION FROM THE ORIGINALLY GIVEN GENERAL FORM?:
y=-2x%5E2%2B12x-4, as given.
y=-2%28x%5E2-6x%2B2%29, the trinomial factor IS NOT FACTORABLE any further!