Consider the parent quadratic function f(x) = x2.(the 2 is an exponent) give the equation of a function that represents a horizontal translation of the parent, that is, it has moved right or left. (many correct examples are possible.) then give the equation of a function that represents a vertical translation of the parent, that is, it has moved up or down. (many correct examples are possible.) finally, give the equation of a reflection of the parent across thex-axis. (only one correct answer exists.)

F(x)=x^2

horizontal:
to translate the function to the left you have to increase x, sort of like g(x)=f(x+1)
so if you insert this directly into the function you get g(x)=(x+1)^2, to move it to the right you would decrease x

vertical:
to translate it vertically you have to change it's y value for every x value by a constant offset
so you get h(x)=x^2+c for some c like +1 to increase y by 1 for every value/move it 1 up

mirror:
to mirror the function over the x-axis you have to switch the sign of all y coordinates of points of your function
simply said multiply the function by -1
so I(x)=-1*(x^2)