Question

For each function,
i) identify the values of the parameters a, h, and k
ii) identify the transformations
iii) use transformations to graph the function and check that it is
correct with a table of values or a graphing calculator

f(x)=(x-1)^2+1

Answer 1

A quadratic function $f(x)=a (x-h)^2+k$ is known as a standard form with real parameters being a,h and k. A graph of this function is a graph of $y=<x^2$ That has undergone some transformations.

If h>0 , the graph shifts toward the right h values and when h<0 graph shifts to the left h values.

When a<0 the graph has been reflected over the x-axis.

When k>0 the graph shifts upward k values and vice versa.