Question

How do you find the domain and range of `F(x) = -2(x + 3)² - 5`?

Answer 1

`x inRR,y in(-oo,-5]`

Explanation:

`"this is a polynomial of degree 2 and is defined for all "`
`"real values of "x`

`"domain is "x inRR`

`"to find the range we require the vertex and if maximum"`
`"or minimum turning point"`

`"the equation of a parabola in "color(blue)"vertex form"` is.

`•color(white)(x)y=a(x-h)^2+k`

`"where "(h,k)" are the coordinates of the vertex and a"`
`"is a multiplier"`

`f(x)=-2(x+3)^2-5" is in this form"`

`"with "(h,k)=(-3,-5)" and "a=-2`

`"since " a <0" then maximum turning point"`

`"range is "y in(-oo,-5]`
graph{-2(x+3)^2-5 [-28.46, 28.5, -14.22, 14.25]}