Final answer:
Transformation of the parent function y=x² can include translations, reflections, and stretching or shrinking. To 'undo' or invert a square, one takes the square root. In kinematics, equations are rearranged to isolate and solve for unknown variables, and projectile motion can be proven to follow a parabolic trajectory.
Step-by-step explanation:
The transformation of the parent function y=x² involves various operations such as translations, reflections, stretchings, and shrinkings. To transform this function, one might add or subtract terms to shift the graph vertically or horizontally, or multiply by a coefficient to stretch or compress it. For example, if we have the function y=x²+2, this represents a vertical translation of the parent function upwards by 2 units.
To address the concept of 'undoing' or inverting a mathematical operation as it is discussed in context, let's say we have a squared term like a² and we want to find the value of 'a'. If a²=c²-b², to find 'a', we take the square root of both sides after rearranging the equation to isolate a².
In kinematics, to solve for an unknown variable like velocity or acceleration using a given equation, one would first need to rear-range the equation to isolate the unknown variable and then perform the necessary algebraic operations.
To prove the trajectory of a projectile is parabolic, one would solve for 't' from the horizontal motion equation x = V_ox*t and substitute it into the vertical motion equation to obtain a quadratic equation in the form y = ax+bx², where a and b are constants determined by the initial velocity components and acceleration due to gravity.