Question

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

Answer 1

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 <=3 or y in (-oo , 3]`

Explanation:

`y= -2 x^2+3 or y= -2 (x-0)^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 :.` 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 RR or x in (-oo,oo)`

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

`y <=3 or y in (-oo , 3]`

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