Find the Intercepts, Vertex, Maximum or minimum and Range for the function n(x)=(x-4)^2-4

Question

​(A) Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

The​ y-intercept is

​(Type an integer or decimal rounded to two decimal places as​ needed.)

B.

There is no​ y-intercept.

Part 2

A.

The​ x-intercepts are

​(Use a comma to separate answers as needed. Type an integer or decimal rounded to two decimal places as​ needed.)

B.

There is no​ x-intercept.

Part 3

​(B)​ Vertex:

enter your response here

​(Type an ordered​ pair.)

Part 4

​(C) The function has a

maximum?

OR minimum?

Part 5

Maximum or minimum​ value:

Part 6

​(D)​ Range:

​(Type an​ inequality, or in interval​ notation.)

Answer 1

(x-4)^2 -4 in vertex form

expand

=x^2-8x+16-4

combine constant terms

=x^2-8x +12, constant term = y-intercept=12

factor

=(x-6)(x-2) in x-intercept form, x=2,6

y intercept is 12 = (0,12)

x intercepts are 2, 6 = (2,0), (6,0)

vertex (4,-4) = minimum point,

no maximum point

minimum=-4, = (4,-4)

both local & global minimum

range is [-4, infinity)

or

-4<x<infinity