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

May 7, 2018

Domain is any real value of x; x in RR or x in (-oo,oo)
Range is any real value of $y$ less or equal to $3$ i.e
$y \le 3 \mathmr{and} y \in \left(- \infty , 3\right]$

#### Explanation:

$y = - 2 {x}^{2} + 3 \mathmr{and} y = - 2 {\left(x - 0\right)}^{2} + 3$ Comparing with vertex

form of equation f(x) = a(x-h)^2+k ; (h,k) being vertex we

find here $h = 0 , k = 3 , a = - 2 \therefore$ Vertex is at $\left(0 , 3\right)$ Since $a$

is negative the parabola opens downward , therefore vertex is the

maximum point $\left(0 , 3\right)$ of the parabola.

Domain is any real value of $x$ i.e $x \in \mathbb{R} \mathmr{and} x \in \left(- \infty , \infty\right)$

Range is any real value of $y$ less or equal to $3$ i.e

$y \le 3 \mathmr{and} y \in \left(- \infty , 3\right]$

graph{-2 x^2+3 [-10, 10, -5, 5]} [Ans]