Question

Gerald graphs the function f(x) = (x – 3)2 – 1. Which statements are true about the graph? Check all that apply.

Answer 1

Answer:

Options 2,3,6 are right

Step-by-step explanation:

Given is a quadratic function as

$(x - 3)^2- 1.$

This is a parabola in vertex form

Vertex = (3,-1)

Open up since leading term is positive

symmetrical about x =3

Range is y≥-1

The function decreases for x<3

Increases for x >3

Hence the correct options are

Option 2, 3, 6

Answer 2

Please use " ^ " to indicate exponentiation.  Then:  f(x) = (x – 3)^2 – 1.
By comparing this equation to                                  y-k  = (x-h)^2
you can see that h=3 and k= -1.  Thus, the vertex is at (3, -1).
The axis of symm. goes thru the vertex, so is x = 3.
The domain is the set of all real numbers.
Since the vertex is (3, -1), the smallest value y can take on is -1.  Thus, the range is [-1, infinity)