SOLUTION: kindly answer this one with solution Find the domain and range of y = x2 +3x -2?

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Question 466981: kindly answer this one with solution
Find the domain and range of y = x2 +3x -2?


Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find the domain and range of y = x^2 +3x -2?
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Domain: All Real Numbers (ARN)
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Since the vertex occurs at x = -b/(2a) = -3/(2) = -3/2
and f(-3/2) = (3/2)^2+3(-3/2)-2 = 9/4 - 18/4 - 8/4 = -17/4,
Range is ARN >= -17/4
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graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2%2B3x-2%29
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Cheers,
Stan H.


Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
y = x² + 3x - 2

We find the vertex as the point

V%28-b%2F%282a%29%2Cf%28-b%2F%282a%29%29+%29

V%28-3%2F%282%2A1%29%2Cf%28-3%2F%282%2A1%29%29+%29

V%28-3%2F2%2Cf%28-3%2F2%29+%29

V%28-3%2F2%2C%28-3%2F2%29%5E2%2B3%28-3%2F2%29-2+%29

V%28-3%2F2%2C9%2F4-9%2F2-2+%29

V%28-3%2F2%2C9%2F4-18%2F4-8%2F4+%29

V%28-3%2F2%2C-17%2F4%29





Here is the graph:



To find the DOMAIN draw a HORIZONTAL line near the
x-axis and that extends from the LEFT-most part of 
the graph to the RIGHT-most part of the graph.  That's
the HORIZONTAL green line drawn below:



The graph would extend infinitely far to the right
and infinitely far to the right, if all of the graph could
be drawn, so would the hroizontal green line.  So the
DOMAIN is:

(-infinity,infinity)


---

To find the RANGE draw a VERTICAL line near the
y-axis and that extends from the LOWEST part of 
the graph to the UPPERMOST part of the graph.  That's
the VERTICAL green line drawn below:



The RANGE is
[-17%2F4,infinity)

It extends from the vertex at -17%2F4 to +infinity.
Because it includes its lowest point, the vertex,
we use "[".

Edwin