The correct statements are ,
- The domain is all real numbers.
- The function is negative over (–6, –2).
- 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).
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