g(x)= (x+2)^2+1

Question

Using the graph of f(x)=x^2 as a guide, describe the transformations, and then graph each function.

Answer 1

The standard form of a parabolic function is given by the function:

f(x) = a(x - h)² + k

The point (h,k) is the vertex of the parabola

a describes how the parabola opens:  Positive opens up, negative opens down, If the absolute value of a is greater than one it is stretched vertically, If the absolute value of a is less than one it is stretched horizontally

Looking at your equation:

h is -2 (The number being subtracted from x

k is 1 (The number being added to the square term

a is 1 (Since nothing is written, the a value is understood to be one)

The vertex is at (-2,1), which means the graph has been moved left two and up one.