Question

The graph of the function f(x) = (x + 6)(x + 2) 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 function is increasing over (–∞, –4).
The function is negative over (–6, –2).

Answer 1

the answers to the question would be number 2, number 3, and number 5

Answer 2

The correct statements are ,

1. The domain is all real numbers.
2. The function is negative over (–6, –2).
3. The axis of symmetry is x = –4. .

Given that,

Function f(x) = (x + 6)(x + 2) .

We have to find,

The vertex, axis of symmetry, domain for the given function f(x).

• The vertex represents the lowest point on the graph or the minimum value of the quadratic function.

Which is x = -6 for the function f(x).

So, The vertex is the minimum value x = -6.

• The axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetric.

Axis of symmetry = $\frac{-b}{2a}$

So, f(x) = (x + 6)(x + 2) = $x^{2} +8x +12$

Then, Axis of symmetry = $\frac{-8}{2(1)}$ = -4.

• The domain of a quadratic function f(x) is the set of x -values for which the function is defined.

The domain for  f(x) = (x + 6)(x + 2) is -6 and -2 which are all real number.

• A function is called monotonically increasing (also increasing or non-decreasing).

The function is increasing over  (–∞, –6) for function f(x) = (x + 6)(x + 2) .

• The y-value decreases as the x-value increases: For a function y = f(x): when $x_1$ < $x_2$ then, The function is negative over (–6, –2).

For more information about Quadratic equation click the link given below.

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