1. The problem is to identify the equation that best matches the given graph of a parabola. 2. The graph shows a parabola with vertex at approximately $(-3, 3)$ and it opens downward. 3. The vertex form of a parabola's equation is $$y = a(x - h)^2 + k$$ where $(h, k)$ is the vertex and $a$ determines the direction and width of the parabola. 4. Since the vertex is $(-3, 3)$, the equation must be of the form $$y = a(x + 3)^2 + 3$$ because $h = -3$ means $(x - (-3)) = (x + 3)$. 5. The parabola opens downward, so $a$ must be negative. 6. The options with vertex $(-3, 3)$ are: - $y = -0.2(x + 3)^2 + 3$ - $y = 0.2(x + 3)^2 + 3$ 7. Since the parabola opens downward, the correct choice is $$y = -0.2(x + 3)^2 + 3$$. 8. To verify, check the y-intercept by plugging $x=0$: $$y = -0.2(0 + 3)^2 + 3 = -0.2(9) + 3 = -1.8 + 3 = 1.2$$ which matches the graph crossing near $(0,1)$. Final answer: $$y = -0.2(x + 3)^2 + 3$$