Parabola Direction 3D217B

1. The problem is to understand why the coefficient $a$ in a quadratic function $y = ax^2 + bx + c$ determines the direction of the parabola. 2. The formula for a quadratic function is $$y = ax^2 + bx + c$$ where $a$, $b$, and $c$ are constants. 3. Important rule: If $a > 0$, the parabola opens upwards (like a U). If $a < 0$, the parabola opens downwards (like an upside-down U). 4. So, if the parabola is downwards, the coefficient $a$ must be negative. 5. This is because the sign of $a$ affects the curvature of the parabola. A negative $a$ flips the parabola upside down. 6. Therefore, for a downwards parabola, $a < 0$. This explains why $a$ should be negative for a downwards parabola.