1. The problem is to identify which quadratic equation best matches the given graph. 2. The general form of a quadratic equation is $$y = ax^2 + bx + c$$ where $a$ determines the concavity (up if $a>0$, down if $a<0$), $b$ affects the slope, and $c$ is the y-intercept. 3. From the graph description, the parabola opens downwards, so $a$ must be negative. 4. The y-intercept is near 9, so $c \approx 9$. 5. The parabola passes near (1,7), so substituting $x=1$ and $y=7$ into the equation helps verify the constants. 6. Test option 1: $y = -0.6x^2 - 2x + 9$ Substitute $x=1$: $$y = -0.6(1)^2 - 2(1) + 9 = -0.6 - 2 + 9 = 6.4$$ which is close to 7. 7. Test option 3: $y = -0.6x^2 - 2x + 7.3$ Substitute $x=1$: $$y = -0.6 - 2 + 7.3 = 4.7$$ which is less than 7. 8. Options 2 and 4 have positive $a$, so they open upwards, which contradicts the graph. 9. Therefore, the best match is option 1: $$y = -0.6x^2 - 2x + 9$$ Final answer: $$\boxed{y = -0.6x^2 - 2x + 9}$$