x2+2x+1=y
or
y=x2
In this function the domain is x equals real values and the range is y equals all real values provided y is more than or equal to zero.
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y = ax2 + bx + c
If the highest exponent of independent variable(say x) is 2 and the highest exponent of dependent variable(say y) is 1 and x and y are not multiplied, then the function is quadratic. For example: 3x-y+x2= 2y-5x+7 represents a quadratic function but y= xy+x2+5 doesn't represent a quadratic function.
A quadratic function will have a degree of two.
A quadratic function is a second degree polynomial, that is, is involves something raised to the power of 2, also know as squaring. Quadratus is Latin for square. Hence Quadratic.
It follows from the definition of a quadratic funtcion.