Question

How do you find the domain and range for `y=5/4(x+2)^2 -1`?

Answer 1

`x inRR,y in[-1,oo)`

Explanation:

`"this is a quadratic and is defined for all real values of "x`

`"domain is "x inRR`

`(-oo,oo)larrcolor(blue)"in interval notation"`

`"to find the range we require to find the vertex and if it is"`
`"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"`

`y=5/4(x+2)^2-1" is in this form"`

`"with "(h,k)=(-2,-1)larrcolor(red)"vertex"`

`"since "a>0" then minimum turning point "uuu`

`"range is "y in[-1,oo)`
graph{5/4(x+2)^2-1 [-10, 10, -5, 5]}