\begin{tabular}{l} Graph the equation. \\ \( \qquad y=3|x+3| \) \\ \hline\end{tabular}

While I cannot directly graph the equation, I can guide you through the process of graphing the equation \( y = 3|x + 3| \). ### Step-by-Step Guide to Graphing \( y = 3|x + 3| \) 1. **Identify the Vertex**: - The expression inside the absolute value, \( x + 3 \), equals zero when \( x = -3 \). This point is the vertex of the graph. - At \( x = -3 \): \[ y = 3|(-3) + 3| = 3|0| = 0 \] - So, the vertex is at the point \((-3, 0)\). 2. **Determine the Slope**: - The absolute value function creates a V-shape. The slope of the lines will change at the vertex. - For \( x < -3 \) (to the left of the vertex), the equation simplifies to: \[ y = 3(-x - 3) = -3x - 9 \] - For \( x > -3 \) (to the right of the vertex), the equation simplifies to: \[ y = 3(x + 3) = 3x + 9 \] 3. **Calculate Points**: - Choose a few values of \( x \) to find corresponding \( y \) values: - For \( x = -4 \): \[ y = 3|-4 + 3| = 3| -1 | = 3 \] Point: \((-4, 3)\) - For \( x = -2 \): \[ y = 3|-2 + 3| = 3|1| = 3 \] Point: \((-2, 3)\) - For \( x = -6 \): \[ y = 3|-6 + 3| = 3|-3| = 9 \] Point: \((-6, 9)\) - For \( x = 0 \): \[ y = 3|0 + 3| = 3|3| = 9 \] Point: \((0, 9)\) 4. **Plot the Points**: - Plot the points \((-3, 0)\), \((-4, 3)\), \((-2, 3)\), \((-6, 9)\), and \((0, 9)\) on a coordinate plane. 5. **Draw the V-Shape**: - Connect the points to form a V-shape, with the vertex at \((-3, 0)\) and the arms extending upwards. ### Summary The graph of \( y = 3|x + 3| \) is a V-shape with its vertex at \((-3, 0)\) and slopes of -3 to the left and +3 to the right. You can use graphing software or a graphing calculator to visualize it more accurately.