SOLUTION: y=x²+12x+2

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Question 188654: y=x²+12x+2
Found 2 solutions by solver91311, Alan3354:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


What a lovely little quadratic function. Thank you so very much for sharing it with us. Now, would you care to also share with us what you wanted to do with or know about this? Do you want to graph it? Find the x- or y-intercepts? Find the axis of symmetry? Find the vertex? Describe the character of the function at the vertex? Perhaps you need the function describing the rate of change of this function, or even the area between the x-axis and the curve between some pair of limits.

Perhaps you wanted us to guess what you wanted, and then, if you are lucky, we will give you the correct help. Or maybe you wanted us to tell you everything so that you could pick out what you need -- never mind that doing so would be a good deal of perhaps unnecessary work for one of us.

On the page you go through to get to the link allowing you to submit a question, there are a set of rules for use of this site. Please take the time to read them next time you wish to avail yourself of the volunteer tutors' time. Pay particular attention to the parts that refer to asking the question completely so that we don't have to guess what you want. And don't forget the part about showing the work you have done so far.

Do have a nice day now.

John


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
y=x²+12x+2
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B12x%2B2+=+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=%2812%29%5E2-4%2A1%2A2=136.

Discriminant d=136 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+136+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+136+%29%29%2F2%5C1+=+-0.169048105154699
x%5B2%5D+=+%28-%2812%29-sqrt%28+136+%29%29%2F2%5C1+=+-11.8309518948453

Quadratic expression 1x%5E2%2B12x%2B2 can be factored:
1x%5E2%2B12x%2B2+=+%28x--0.169048105154699%29%2A%28x--11.8309518948453%29
Again, the answer is: -0.169048105154699, -11.8309518948453. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B12%2Ax%2B2+%29

so it's -6 +- sqrt(34)
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If you want a better graph, dl the free software at
www.padowan.dk.com/graph/