Question

For the function f(x) = –2(x + 3)2 − 1, identify the vertex, domain, and range.

Answer 1

use desmos.com

Answer 2

f(x) is a polynomial function (why? cuz it has whole number powers of x only, and no other complex terms), and a polynomial is always continuous on the interval (-∞,+∞).

that is for your domain.

Answer 3

the vertex of a parabola (your function is a parabola)
in a form of: f(x)=a(x-h)²+k
is the point: (h,k)

Answer 4

can you identify the vertex here?
\(f(x)=-2(x+3)^2-1\)

Answer 5

Is it (3, -1)?

Answer 6

almost....

\(f(x)=-2(x+3)^2-1\)

\(f(x)=-2(x-\color{red}{-3})^2-\color{red}{1}\)

Answer 7

it is (-3,1)

Answer 8

and the domain is all real numbers (as I have reviously explained)

Answer 9

Now, your leading coefficient is negative, that means your parabola opens down and goes into -∞.....
BUT, the range will be limited, and it is limited by the vertex because vertex is the maximum point (in any case when parabola opens down)

Answer 10

what is the y-value of your vertex?
that is where the range ends....

and it starts from negative infinity

Answer 11

Wouldn't the range be y is equal to or lesser than -3

Answer 12

-3 is the x-coordinate of the vertex....

Answer 13

so not to -3, but to?

Answer 14

This it is -1

Answer 15

yes, the range is y≤-3

Answer 16

oh sorry

Answer 17

I mean y≤1

Answer 18

ok thank you

Answer 19

yw