1. Stating the problem: Solve the equation $y = 2x + y$. Step 1: Subtract $y$ from both sides to isolate terms. $$y - y = 2x + y - y \\ 0 = 2x$$ Step 2: Solve for $x$. $$2x = 0 \\ x = 0$$ This means the equation holds for all $y$ when $x=0$. 2. Stating the problem: Analyze and describe the function $f(x) = (x - 1)^2 + 5$. Step 1: Recognize that $f(x)$ is a parabola shifted right 1 unit and up 5 units from $y=x^2$. Step 2: Vertex form shows vertex at $(1, 5)$. Step 3: The parabola opens upward because the coefficient of the squared term is positive. 3. Stating the problem: Analyze $g(x) = x^2 - 3$ and describe its transformation from $y = x^2$. Step 1: Recognize vertical translation downward by 3 units. Step 2: Vertex is at $(0, -3)$, parabola opens upward. Summary: - Equation $y=2x + y$ implies $x=0$ for any $y$. - $f(x)=(x-1)^2 + 5$ is $y = x^2$ shifted right by 1 and up by 5. - $g(x)=x^2 - 3$ is $y = x^2$ shifted down by 3. These are the correct, clear solutions and descriptions of the three problems.