How do you find the domain and range of $y=x^2 +2x -5$ ?

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Answer 1 · 2017-07-09T03:09:04

Domain: $(-oo, +oo)$
Range: $[-6, +oo)$

$y=x^2+2x-5$

$y$ is defined $forall x in RR$
Hence the domain of $y$ is $(-oo, +oo)$

$y$ is a quadratic function of the form $ax^2+bx+c$

The graph of $y$ is a parabola with vertex where $x=(-b)/(2a)$

Since the coefficient of $x^2>0$ the vertex will be the absolute minimum of $y$

At the vertex $x= (-2)/(2xx1) = -1$

$:. y_min = y(-1) = 1-2-5 = -6$

Since $y$ has no upper bound the range of $y$ is [-6, +oo)

As can be seen on the graph of $y$ below.

graph{x^2+2x-5 [-16.02, 16.02, -8.01, 8.01]}

How do you find the domain and range of y=x^2 +2x -5y=x^2 +2x -5?