SOLUTION: for the function f(x)=3x^2+23x-14 find the domain and range

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Question 605082: for the function f(x)=3x^2+23x-14
find the domain and range
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
for the function f(x)=3x^2+23x-14
find the domain and range
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Domain: All Real Numbers
----------------------------
Range: ?
Find the vertex:
x = -b/(2a) = -23/(6)
f(-23/6) = 3(-23/6)^2 + 23(-23/6) -14 = -58.08
Since the parabola opens up, the range is
"All Real Numbers >= -58.08".
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graph%28400%2C400%2C-30%2C30%2C-65%2C80%2C3x%5E2%2B23x-14%29
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Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I can put any number I want in for x, (+) or (-),
and I still get out y's, so the domain is + infinity
to - infinity
----------------
The curve is a parabola with a minimum at it's vertex, and
the vertex is at +x+=+-b%2F%282a%29+ where
+a+=+3+
+b+=+23+
Vertex is at +x+=+-23%2F%282%2A3%29+
+x+=+-23%2F6+
Plug this into equation to find +f%28x%29+
+f%28-23%2F6%29+=+3%2A%28-23%2F6%29%5E2+%2B+23%2A%28-23%2F6%29+-+14+
+f%28-23%2F6%29+=+529%2F12+-+529%2F6+-+84%2F6+
+f%28-23%2F6%29+=+-529%2F12+-+168%2F12+
+f%28-23%2F6%29+=+-697%2F12+
So, the range is + infinity to -697/12
Here's the plot:
+graph%28+400%2C+400%2C+-12%2C+12%2C+-60%2C+20%2C+3x%5E2+%2B+23x+-+14+%29+