Identify the domain and range of the function f (x) = 2x2 - 6x - 9.

Range is the y values or ouputs

domain is inputs or x vvalues

we can use any x value

but at a certain y value, w can't go below that

find thatminimum

find the vertex

for

ax^2+bx+c

the x value of the vertex is

-b/2a

plug that in to the equaiton to get the y value

-b/2a = - (-6) / (2*2) = 6/4=3/2

plug that in

2 (3/2) ^2-6 (3/2) - 9

2 (9/4) - 9-9

9/2-18

4.5-18

-13.5

domain=all real numbers

range=from - 13.5 to positive infinity