What is the parent function for the following equation
F(x)=(x-2)(x-1)
x^2
F(x) = (x - 3/2)^2 - 1/4
If f(x) = x^2 then F(x) = f(x - 3/2) - 1/4
quadratic
The parent function for the given equation F(x) = (x-2)(x-1) is the quadratic function, f(x) = x^2.
To find the parent function for the equation F(x) = (x-2)(x-1), we need to understand what a parent function is.
A parent function is the most basic form of a function that represents a specific type of function. For instance, the parent function of a quadratic function is f(x) = x^2.
In our given equation, F(x) = (x-2)(x-1), we have a quadratic function in factored form. The factored form of a quadratic function is f(x) = (x-a)(x-b), where a and b are the x-intercepts or roots of the function.
Comparing the given equation F(x) = (x-2)(x-1) to the factored form, we can see that a = 2 and b = 1.
So, the parent function for the equation F(x) = (x-2)(x-1) is the general form of a quadratic function: f(x) = x^2.
In summary, the parent function for the equation F(x) = (x-2)(x-1) is f(x) = x^2.