Final answer:
If 'a' is negative in a quadratic equation, the parabola opens downwards, and the vertex represents the maximum point. These factors determine the graph's shape, not the calculation of the roots.
Step-by-step explanation:
If a is negative in the quadratic equation ax² + bx + c, we know two key things:
- The parabola that represents the equation on a graph will open downwards because the coefficient a determines the direction of the opening.
- The vertex of the parabola will be its maximum point since the parabola opens downwards.
These characteristics about the quadratic equation can be understood in the context of the standard form of a quadratic equation, which is ax² + bx + c = 0. The solution or roots for any quadratic equation can be calculated using the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a). However, the sign of a alone does not affect the calculation of the roots; it primarily influences the shape and position of the parabola.