Question

Which is the graph of f(x) = –(x + 3)(x + 1)?

On a coordinate plane, a parabola opens down. It goes through (0, negative 3), has a vertex at (2, 1), and goes through (4, negative 3).

On a coordinate plane, a parabola opens down. It goes through (negative 3, 0), has a vertex at (negative 2, 1), and goes through (negative 1, 0).

On a coordinate plane, a parabola opens up. It goes through (negative 4, 3), has a vertex at (negative 2, negative 1), and goes through (0, 3).

On a coordinate plane, a parabola opens up. It goes through (0, 3), has a vertex at (2, negative 1), and goes through (4, 3).

Answer 1

1.) maximum value

2.) for no values of x

3,) when x > -1

4.) all real numbers

5.) all numbers less than or equal to 0

I did the workExplanation:

i just did this on edg

Answer 2

The 2nd answer choice is the correct one.

Explanation:

f(x) = –(x + 3)(x + 1), when multiplied out, becomes f(x) = -(x^2 + 4x + 3), or

f(x) = -x^2 - 4x - 3. Because of the - sign, the graph opens downward.

Because of the factor (x + 3), the graph goes through (-3, 0).

Because of the factor (x + 1), the graph goes through (-1, 0).

The vertex is located horizontally exactly betwen x = -3 and x = -1, that is, at x = -2. Since f(-2) = -(-2)^2 - 4(-2) - 3, the max value of f is -4 + 8 - 3, or 1. Thus, the vertex is located at (-2, 1). This matches the 2nd answer choice.