How do you find the domain and range of $Y=-x^2+4x-1$ ?

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Answer 1 · 2017-05-28T18:46:20

See explanation.

The function is a polynomial, so it is defined for all real values of $x$ . This means that the domian is $D=RR$

To calculate the range we have to find the vertex of the parabola:

$p=(-b)/(2a)=(-4)/-2=2$

$q=f(p)=-2^2+4*2-1=3$
graph{-x^2+4x-1 [-11.25, 11.25, -5.625, 5.625]}

From the graph we see that the range is $(-oo;3]$

How do you find the domain and range of Y=-x^2+4x-1Y=-x^2+4x-1?