## Calculus 10th Edition

The sloping line is the derivative ($f'(x)$) while the parabola is the parent function ($f(x)$).
The equation of a parabola is $y=ax^2+bx+c$ and the derivative of the general equation of a parabola is $y'=2ax+b$ hence the parabola is the parent function while the sloping line is the derivative. Furthermore, the derivative of the general equation of a sloping line ($y=mx+b$ ) is $m$ hence the derivative of a sloping line would be a horizontal line of equation $y=m$; due to this, the sloping line cannot be the parent function.