Question 528925: I need to graph this and I don't know how. X^2 + 100 = 27x I need at least four points.
thank you for your help!
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! I need to graph this and I don't know how. X^2 + 100 = 27x I need at least four points.
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rewrite equation:
y=x^2-27x+100
complete the square:
y=(x^2-27x+182.25)+100-182.25
y=(x-13.5)^2-82.25)
This is an equation of a parabola of the standard form: y=(x-h)^2+k, with (h,k) being the (x,y) coordinates of the vertex.
For given equation:
vertex: (13.5,-82.25)
so, now you have one point for a graph
..
Finding x-intercepts:
set y=0
(x-13.5)^2-82.25=0
(x-13.5)^2=82.25
take sqrt of both sides
x-13.5=±√(82.25)≈±9.069
x≈13.5±9.069
x≈22.57
or
x≈4.43
You have the following 3 points with which you can draw the graph:
(13.5,-82.25) (vertex)
(22.57,0) x-intercept
(4.43,0) x-intercept
You should be able to draw a good graph with these three points, but if you need more, plug in convenient x-values into the first equation listed above.
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