Question

For the function f(x) = –(x + 1)2 + 4, identify the vertex, domain, and range.

Answer 1

Welcome to OpenStudy!

For clarity, I'm going to edit your f(x) = –(x + 1)2 + 4 .

It should appear as follows: f(x) = –1(x + 1)^2 + 4, or

Answer 2

\[f(x) = –1(x + 1)^2 + 4\]

Answer 3

Please compare your function, above, with the vertex form of the equation of a parabola:

\[f(x) = a(x - h)^2 + k\]

Answer 4

By inspection, determine the values of a, h and k.

Then your vertex is at (h,k)

What value do you find for the coefficient a?

If a is +, your parabola opens UP; if -, your parabola opens DOWN.

Can you now graph the vertex?

Can you now determine whether your parabola opens up or down?

Can you now sketch this parabola (the graph of f(x) = –1(x + 1)^2 + 4)?

Answer 5

Thanks @mathmale

Answer 6

My pleasure!