SOLUTION: can you create your own quadratic equation and show how it would be solved by graphing, factoring, the quadratic formula, and by completing the square.

Algebra ->  Linear-equations -> SOLUTION: can you create your own quadratic equation and show how it would be solved by graphing, factoring, the quadratic formula, and by completing the square.       Log On


   

Question 668932: can you create your own quadratic equation and show how it would be solved by graphing, factoring, the quadratic formula, and by completing the square.
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
Since you get to choose your own, work backward and pick simple roots.
Lets say, 2 and 4
...
(x-2)(x-4) : which is the factored form
Therefore, the equation is: x%5E2+-+6x+%2B+8+=+0
...
Completing the square
x%5E2+-+6x+%2B+9+=+-8+%2B+9
(x-3)(x-3) = 1
%28x-3%29%5E2+=+1
sqrt%28x-3%29%5E2+=+%2B-sqrt%281%29
x+-+3+=+%2B-sqrt%281%29
x+=+3+%2B-+sqrt%281%29
x = 3+1 = 4
x = 3-1 = 2
...
Quadratic formula
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B8+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-6%29%5E2-4%2A1%2A8=4.

Discriminant d=4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+4+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+4+%29%29%2F2%5C1+=+4
x%5B2%5D+=+%28-%28-6%29-sqrt%28+4+%29%29%2F2%5C1+=+2

Quadratic expression 1x%5E2%2B-6x%2B8 can be factored:
1x%5E2%2B-6x%2B8+=+%28x-4%29%2A%28x-2%29
Again, the answer is: 4, 2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B8+%29

.....................
Delighted to help.
-Reading Boosters
Wanting for others what we want for ourselves.
www.MyHomeworkAnswers.com