Question

If you shift the quadratic parent function, F(x)=x^2 , down 9 units, what is the equation of the new function?

A. G(x)=x^2+9
B. G(x)=(x−9)^2
C. G(x)=x^2−9
D. G(x)=(x+9)^2

Answer 1

The equation of the new function when shifting the quadratic parent function F(x)=x^2 down by 9 units is G(x)=x^2−9.

Step-by-step explanation:

If you shift the quadratic parent function F(x)=x^2 down 9 units, the equation of the new function would reflect a vertical translation downwards on the y-axis. A down shift by 9 units translates to subtracting 9 from the original function's value for each x. Therefore, the new function, G(x), would be G(x)=x^2−9. This is represented mathematically as taking the original function and subtracting 9 from it, resulting in a new function that graphically appears as the same parabola, just shifted down 9 units on the coordinate plane.