SOLUTION: Ok, I'm going to try this one more time... I need help solving AND factoring the following equation (taken from Bittinger's College Algebra: Graphs and Models 4th Edition, page

Algebra ->  Graphs -> SOLUTION: Ok, I'm going to try this one more time... I need help solving AND factoring the following equation (taken from Bittinger's College Algebra: Graphs and Models 4th Edition, page      Log On


   

Question 215713: Ok, I'm going to try this one more time...
I need help solving AND factoring the following equation (taken from Bittinger's College Algebra: Graphs and Models 4th Edition, page 76, problem number 39.)
+y+=+-x%5E2+%2B+2x+%2B+3
A point to remember: The x^2 is NEGATIVE, and the 2x and 3 are both POSITIVE.
Thank you in advance!
Found 2 solutions by nerdybill, drj:
Answer by nerdybill(7384) About Me  (Show Source):
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
y+=+-x%5E2+%2B+2x+%2B+3

Step 1. Let's factor out negative 1 so now we have y=-1%28x%5E2-2x-3%29

Step 2. We need two integers m and n such that their sum is -2=m+n and their product mn=-3.

Step 3. The integers are -3 and 1. Then, x%5E2-3x-3=%28x-3%29%28x%2B1%29

Step 4. ANSWER: y = -x^2 + 2x + 3=-1*(x-3)(x+1) when y=0 we are finding x as solutions where it intersects the x-axis or in our case (x-3)=0 and (x+1)=0 or x=3 and x=-1.

You can also use the quadratic formula given as x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=-1, b=2 and c=3.

The graph is shown below:

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B2x%2B3+=+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=%282%29%5E2-4%2A-1%2A3=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+16+%29%29%2F2%5C-1+=+-1
x%5B2%5D+=+%28-%282%29-sqrt%28+16+%29%29%2F2%5C-1+=+3

Quadratic expression -1x%5E2%2B2x%2B3 can be factored:
-1x%5E2%2B2x%2B3+=+-1%28x--1%29%2A%28x-3%29
Again, the answer is: -1, 3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B2%2Ax%2B3+%29



I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J