Question

. Identify the vertex of f(x) = 3|x + 71 - 27.

a. (3,7)
(b) (7,-27)
c. (7,3)
d. (-7,-27)

Answer 1

The vertex of the function f(x) = 3|x + 71 - 27 is (-71, -27), found by setting the expression inside the absolute value to zero and calculating the corresponding y-value.

Step-by-step explanation:

The question at hand asks to identify the vertex of the function f(x) = 3|x + 71 - 27. In the context of absolute value functions, the vertex can be found by considering the expression inside the absolute value symbol. The vertex corresponds to the point at which the expression inside the absolute value is zero, and the function changes direction.

In this case, we set x + 71 = 0, which simplifies to x = -71. Plugging this value back into the function, we get f(-71) = 3|0| - 27 = -27. Therefore, the vertex of the function is at the point (-71, -27), which corresponds to answer choice (d).