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<h2>Answer:</h2>
The vertex of the function is:
(-2,-2)
<h2>Step-by-step explanation:</h2>We are given a absolute value function f(x) in terms of variable "x" as:
We know that for any absolute function of the general form:
the vertex of the function is : (h,k)
and if a<0 the graph of function opens downwards.
and if a>0 the graph of the function opens upwards.
Hence, here after comparing the equation with general form of the equation we see that:
a= -1<0 , h= -2 and k= -2
Since a is negative , hence, the graph opens down .
Hence, the vertex of the function is:
(-2,-2)
The function is
f(x) = (1/3)x² + 10x + 8
Write the function in standard form for a parabola.
f(x) = (1/3)[x² + 30x] + 8
= (1/3)[ (x+15)²- 225] + 8
= (1/3)(x+15)² -75 + 8
f(x) = (1/3)(x+15)² - 67
This is a parabola with vertex at (-15, -67).
The axis of symmetry is x = -15
The curve opens upward because the coefficient of x² is positive.
As x -> - ∞, f -> +∞.
As x -> +∞, f -> +∞
The domain is all real values of x (see the graph below).
Answer: The domain is (-∞, ∞)
f(x) = (1/3)x² + 10x + 8
Write the function in standard form for a parabola.
f(x) = (1/3)[x² + 30x] + 8
= (1/3)[ (x+15)²- 225] + 8
= (1/3)(x+15)² -75 + 8
f(x) = (1/3)(x+15)² - 67
This is a parabola with vertex at (-15, -67).
The axis of symmetry is x = -15
The curve opens upward because the coefficient of x² is positive.
As x -> - ∞, f -> +∞.
As x -> +∞, f -> +∞
The domain is all real values of x (see the graph below).
Answer: The domain is (-∞, ∞)