1. The problem asks to determine which statement about the functions f and g is true based on their graphs. 2. From the description, g(x) is a parabola with vertex at (-2, 0) and passes through (0, 4). This means: - The vertex form of g(x) is $$g(x) = a(x + 2)^2 + 0$$ - Since g(0) = 4, substitute x=0: $$4 = a(0 + 2)^2 = 4a \implies a = 1$$ - So, $$g(x) = (x + 2)^2$$ - Therefore, $$g(-2) = (-2 + 2)^2 = 0^2 = 0$$ 3. Similarly, f(x) is a parabola with vertex at (2, 0) and passes through (0, 4): - Vertex form: $$f(x) = b(x - 2)^2 + 0$$ - Substitute x=0: $$4 = b(0 - 2)^2 = 4b \implies b = 1$$ - So, $$f(x) = (x - 2)^2$$ - Therefore, $$f(0) = (0 - 2)^2 = (-2)^2 = 4$$ 4. Now check the statements: - f(0) = 2 and g(-2) = 0 → f(0) = 4, so false - f(0) = 4 and g(-2) = 4 → g(-2) = 0, so false - f(2) = 0 and g(-2) = 0 → f(2) = (2-2)^2 = 0, g(-2) = 0, true - f(-2) = 0 and g(-2) = 0 → f(-2) = (-2-2)^2 = 16, false 5. The true statement is: f(2) = 0 and g(-2) = 0.