Question

What is the domain and range of `y=-3(x-10)^2+5`?

Answer 1

Domain: `x in RR or (-oo,oo)`
Range: `y<=5 or [-oo,5]`

Explanation:

`y= -3(x-10)^2+5` . This is vertex form of equation of parabola

having vertex at `(10,5)` [ Comparing with vertex form of

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

here `h=10 , k=5 , a=-3`] . Since `a` is negative the parabola

opens downward , vertex is the maximum point of `y`.

Domain: Any real number of `x` is possible as input.

So Domain: `x in RR or (-oo,oo)`

Range: Any real number of `y<=5 or [-oo,5]`

graph{-3(x-10)^2+5 [-20, 20, -10, 10]} [Ans]