SOLUTION: I am having a hard time gettting all of the parts of this problem. Can you please help? Graph the parabola. Identify the vertex, axis, intercepts, domain and range. f(x)=-x

Algebra ->  Rational-functions -> SOLUTION: I am having a hard time gettting all of the parts of this problem. Can you please help? Graph the parabola. Identify the vertex, axis, intercepts, domain and range. f(x)=-x      Log On


   

Question 381581: I am having a hard time gettting all of the parts of this problem. Can you please help?
Graph the parabola. Identify the vertex, axis, intercepts, domain and range.
f(x)=-xsquared+4x-1
I got the vertex: (2,3) but can't figure out how to get the intercepts.
Thank you! :)
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=-x%5E2%2B4x-1
f%28x%29=-%28x%5E2-4x%2B4%29-1%2B4
f%28x%29=-%28x-2%29%5E2%2B3
(2,3) is correct for the vertex.
The vertex lies on the axis of symmetry, x=2.
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To find the x-intercepts, now set f%28x%29=0.
-%28x-2%29%5E2%2B3=0
%28x-2%29%5E2=3
x-2=0+%2B-+sqrt%283%29
highlight%28x=2%2B-+sqrt%283%29%29
Those are the x-intercepts.
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To find the y-intercepts, set x=0 solve for y.
f%28x%29=-%280-2%29%5E2%2B3
f%28x%29=-4%2B3
f%28x%29=-1
(0,-1)
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There are no restrictions on the domain.
Since the parabola opens downwards, the value at the vertex is a maximum.
Domain:(-infinity,infinity)
Range:(-infinity,3]
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