Answer:
The parent function of f(x) = x^2 is a quadratic function.
A quadratic function is a polynomial function of the second degree, meaning that its highest degree term is x^2. The general form of a quadratic function is:
f(x) = ax^2 + bx + c
where a, b, and c are constants. In the case of the parent function f(x) = x^2, the coefficients of b and c are both 0, so the equation simplifies to f(x) = ax^2.
The graph of a quadratic function is a curve called a parabola, which is either U-shaped or inverted U-shaped depending on the sign of the leading coefficient a. In the case of the parent function f(x) = x^2, the leading coefficient is positive, which means that the parabola opens upward. The vertex of the parabola is located at the origin (0,0), and the axis of symmetry is the y-axis.
Quadratic functions are used to model a wide range of physical and mathematical phenomena, including projectile motion, the area of a square, and the behavior of certain types of financial investments and business models.