Identify the vertex, axis of symmetry, maximum or minimum, and domain and range of each function:
f(x)=4(x+2)^2-6

Question

Identify the vertex, axis of symmetry, maximum or minimum, and domain and range of each function:
f(x)=4(x+2)^2-6

anonymous · Answer

Your equation is in vertex form f(x)=a(x-h)^2+k 

(h,k) is the vertex, so can you see what the vertex would be?

anonymous · Answer

Ok, would it be -2, 6?

anonymous · Answer

(-2,-6) i mean?

anonymous · Answer

Yes. And the axis of symmetry is just x=h

so x=-2

anonymous · Answer

ok, and i know the minimum is when the parabola opens up and maximum is when it opens down. Would the minimum be -6?

anonymous · Answer

Yes, minimum value of -6 at x=-2.

Domain of these functions is always all real numbers

anonymous · Answer

Ok, and would the range be -2? Im trying to use this problem as a guide for the others :)

anonymous · Answer

Range is all the y values, you see the vertex is at (-2,-6) and the parabola opens up, so the range is gonna be -6 to infinity $$[-6,\infty)$$

anonymous · Answer

Ohhhhh, ok, that makes so much sense now, thank you so much!!! :)

anonymous · Answer

You're welcome