Fill in the blanks to describe the graph of the quadratic function, \( y=-\frac{1}{6} x^{2}-x+8 \). The parabola opens \( [?] \), and its shape is \( \quad \) than \( y=x^{2} \). downward

The quadratic function \( y = -\frac{1}{6}x^{2} - x + 8 \) can be described by filling in the blanks as follows: - **The parabola opens** **downward**, **and its shape is** **wider** **than** \( y = x^{2} \). **Explanation:** 1. **Direction the Parabola Opens:** - The coefficient of \( x^{2} \) is \( -\frac{1}{6} \), which is negative. - A negative coefficient indicates that the parabola opens **downward**. 2. **Shape Comparison to \( y = x^{2} \):** - The coefficient \( -\frac{1}{6} \) has an absolute value less than 1. - When the absolute value of the coefficient \( |a| < 1 \), the parabola is **wider** compared to the standard parabola \( y = x^{2} \). - This means it spreads out more, making it less steep. **Final Description:** The parabola opens **downward**, and its shape is **wider** than \( y = x^{2} \).