Question

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

Answer 1

@phi

Answer 2

That's the equation, right?

Answer 3

yes

Answer 4

So simplify that. What's (x-1) squared?

Answer 5

x^2-2x+1

Answer 6

multiply that by 3 and what do you get

Answer 7

3x^2-6x+3

Answer 8

Oops, hold on.
Sorry, you didn't have to do all that.

For the vertex, since you have (x-1), plug in 1 for x in the original equation. What is your y value?

Answer 9

2

Answer 10

So your vertex would be (1,2).

Answer 11

ya I know that but what is the range

Answer 12

As for domain, are there any values that you can't plug in for x?
As for the range, are there any values that you can't get for y?

Answer 13

i have no idea :/

Answer 14

Well, you can plug in just about everything for x, so the domain would be (-infinity, infinity).
As for range, you can get a y value that is above 2, the y-value in your vertex. So it would be [2, infinity}