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. ${\displaystyle y=x^{2}+bx+c}$ ${\displaystyle y=-x^{2}+bx+c}$ ${\displaystyle b}$ ${\displaystyle c}$

See also

• Quadratic function .