Question

graphing the cubic function quick check
which of the following cubic functions has a point of inflection of (2, -5)? (1 point)
○ $g(x) = -3(x + 2)^3 - 5$
○ $g(x) = -2(x - 2)^3 + 5$
○ $g(x) = 2(x - 2)^3 - 5$
○ $g(x) = (x + 2)^3 + 5$

Explanation:

Step1: Recall inflection point of cubic

A cubic function in the form \( g(x) = a(x - h)^3 + k \) has its point of inflection at \( (h, k) \).

Step2: Analyze each option

• For \( g(x) = -3(x + 2)^3 - 5 \), rewrite as \( g(x) = -3(x - (-2))^3 + (-5) \), so inflection point is \( (-2, -5) \).
• For \( g(x) = -2(x - 2)^3 + 5 \), inflection point is \( (2, 5) \).
• For \( g(x) = 2(x - 2)^3 - 5 \), rewrite as \( g(x) = 2(x - 2)^3 + (-5) \), so inflection point is \( (2, -5) \).
• For \( g(x) = (x + 2)^3 + 5 \), rewrite as \( g(x) = (x - (-2))^3 + 5 \), inflection point is \( (-2, 5) \).

Answer:

\( g(x) = 2(x - 2)^3 - 5 \) (the third option)