# Normal parabola

The normal parabola

The normal parabola is the special parabola with the equation , i.e. the graph of the square function . It is symmetrical to the axis and open at the top. Its vertex lies at the origin of coordinates . The name is derived from the standardization of the parameters in the general parabolic equation to the specific values , , . ${\ displaystyle y = x ^ {2}}$ ${\ displaystyle x \ mapsto x ^ {2}}$${\ displaystyle y}$${\ displaystyle y = ax ^ {2} + bx + c}$${\ displaystyle a = 1}$${\ displaystyle b = 0}$${\ displaystyle c = 0}$

Sometimes the parabola is still referred to as a shifted or mirrored normal parabola even after a shift or a mirroring of the parabola. This then has the general equation or with real coefficients and . In any case, the coefficient 1 or −1 in front of the square term, which determines the opening width of the graph, remains characteristic of the normal parabola. ${\ displaystyle y = x ^ {2} + bx + c}$${\ displaystyle y = -x ^ {2} + bx + c}$${\ displaystyle b}$${\ displaystyle c}$