Explain the effect a horizontal shift has on the given equations

Question

f(x) = a(x - h)² + k

f(x) = ax²+ bx + c

Answer 1

Function transformations are usually only applied when the function is written in the format:

y = A•f(B(x - C)) + D where the function basic "rule" is f(x) for instance

y = 5sin(2(x-1)) + 3 where the basic function rule is sin(x) and "5" is the vertical stretch, "2" is the horizontal stretch, "1" is the horizontal shift and "3" is the vertical shift.

In the case of f(x) = a(x - h)² + k the basic rule is x² and "h" is the horizontal shift. You read the horizontal shift the opposite of what it says so "- h" means a shift of "h" units to the right.

In the case of f(x) = ax²+ bx + c the horizontal shift is hidden and requires some work to discover it. To find it, you would need to calculate -b/2a and then read that number as it is as the horizontal shift.

Example: x² + 2x + 1 so b = 2 and a = 1 so -b/2a = -2(2•1) = -1 so the horizontal shift is -1