How does the coefficient of a affect the way the parabola opens?

The coefficient of ( a ) in the quadratic equation ( y = ax^2 + bx + c ) determines the direction in which the parabola opens. If ( a > 0 ), the parabola opens upwards, creating a "U" shape, while if ( a < 0 ), it opens downwards, resembling an upside-down "U." Additionally, the absolute value of ( a ) affects the width of the parabola; larger values of ( |a| ) result in a narrower parabola, while smaller values lead to a wider shape.