If a quadratic equation opens upward, what can you conclude about its leading coefficient?

A quadratic equation is typically expressed in the standard form ( ax^2 + bx + c = 0 ), where ( a ) represents the leading coefficient. The leading coefficient plays a crucial role in determining the direction in which the parabola opens.

When a quadratic equation opens upward, it indicates that the parabola extends upward from its vertex, creating a "U" shape. This behavior occurs only when the leading coefficient ( a ) is positive. A positive value for ( a ) ensures that as ( x ) moves away from the vertex in either direction, the value of ( y ) (or ( ax^2 + bx + c )) increases, resulting in an upward-opening parabola.

Other options do not align with this characteristic. If ( a ) were zero, the equation would no longer be quadratic but linear, and it wouldn't describe a parabola at all. If ( a ) were negative, the parabola would open downward, exhibiting an inverted "U" shape instead. Lastly, if ( a ) were a complex number, the equation would not produce a real parabola, and its graph would not be defined in the usual coordinate plane context. Hence, understanding the role of the