# How do you find the domain and range of y=-2x^2+3

How do you find the domain and range of $y=-2{x}^{2}+3$?
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Alden Holder
$y=-2{x}^{2}+3$ or $y=-2\left(x-0{\right)}^{2}+3$ Comparing with vertex
form of equation $f\left(x\right)=a\left(x-h{\right)}^{2}+k;\left(h,k\right)$ being vertex we
find here $h=0,k=3,a=-2\therefore$ Vertex is at (0,3) Since a
is negative the parabola opens downward , therefore vertex is the
maximum point (0,3) of the parabola.
Domain is any real value of x i.e $x\in \mathbb{R}$ or $x\in \left(-\mathrm{\infty }\mathrm{\infty }\right)$
Range is any real value of y less or equal to 3 i.e
$y\le 3$ or $y\in \left(-\mathrm{\infty },3\right]$
graph{$-2{x}^{2}+3\left[-10,10,-5,5\right]$} [Ans]