Question

The graph of the function f(x) = x2 + 8x + 12 is shown. Which statements describe the graph? Check all that apply.

The vertex is the maximum value.
The axis of symmetry is x = –4.
The domain is all real numbers.
The range is all real numbers.
The function is increasing over (–∞, –4).
The x-intercepts are at (–6, 0) and (–2, 0).

Answer 1

The axis of symmetry is x = –4.
The domain is all real numbers.
The x-intercepts are at (–6, 0) and (–2, 0).

Answer 2

The graph is missing, so I will post it just at the end of the answer so you can watch it, then we want to see which statements are correct.

The true statements are:

• b) "The axis of symmetry is x = –4"
• c) "The domain is all real numbers."
• f) "The x-intercepts are at (–6, 0) and (–2, 0)."

Now let's analyze each statement in contrast to the given graph:

a) "The vertex is the maximum value."

We can see that the vertex is actually the minimum value, so this is false.

b) "The axis of symmetry is x = –4"

We define the axis of symmetry as the line that divides the graph in two halves, so this is correct.

c) "The domain is all real numbers."

Because there is no restriction (like a denominator that becomes equal to zero or something like that) we can use all the real numbers in this function, so the domain is the set of all real numbers.

d) "The range is all real numbers."

This is false, as we saw, we have a minimum, then the range does not extend to all real numbers.

e) "The function is increasing over (–∞, –4)."

This is false, the function is decreasing on that interval.

f) "The x-intercepts are at (–6, 0) and (–2, 0)."

True, the graph intersepts the x-axis at (-6, 0) and (-2, 0).

If you want to learn more about quadratic functions, you can read:

https://brainly.com/question/24817658