SOLUTION: Quadratic equations are always hard for me to understand and believe me they can kill a day. :o{ Can you help me with the steps with this one. F(x) = -2x^2 + 2x + 8 THanks a

Algebra ->  Test -> SOLUTION: Quadratic equations are always hard for me to understand and believe me they can kill a day. :o{ Can you help me with the steps with this one. F(x) = -2x^2 + 2x + 8 THanks a      Log On


   

Question 356800: Quadratic equations are always hard for me to understand and believe me they can kill a day. :o{
Can you help me with the steps with this one.
F(x) = -2x^2 + 2x + 8
THanks a bunch!
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
They're all the same.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -2x%5E2%2B2x%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=%282%29%5E2-4%2A-2%2A8=68.

Discriminant d=68 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+68+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+68+%29%29%2F2%5C-2+=+-1.56155281280883
x%5B2%5D+=+%28-%282%29-sqrt%28+68+%29%29%2F2%5C-2+=+2.56155281280883

Quadratic expression -2x%5E2%2B2x%2B8 can be factored:
-2x%5E2%2B2x%2B8+=+%28x--1.56155281280883%29%2A%28x-2.56155281280883%29
Again, the answer is: -1.56155281280883, 2.56155281280883. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B2%2Ax%2B8+%29

----------
x+=+-1%2F2+%2B+sqrt%2817%29%2F2
x+=+-1%2F2+-+sqrt%2817%29%2F2

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
F(x) = -2x^2 + 2x + 8
----
You did not say what you want to do with this quadratic.
---
Graph:
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C-2x%5E2%2B2x%2B8%29
===================================================
Y-intercept: If x = 0, y = 8
X-intercept: If y = 0, x = ?
Solve -2x^2+2x+8 = 0
-2(x^2-x-4) = 0
Quad. Formula:
x = [1 +- sqrt(1-4*-4)/2
x = [1+-sqrt(17)]/2
------------------------
Cheers,
Stan H.