Either by hand or with a graphing calculator, Desmos or Geogebra , graph the following functions. Pay particular attention to how the graphs are related. What do they have in common? What is different? What is making the graphs different?
a) \(f(x) = x^2\)
b) \(f(x) = x^2 +2\)
c) \(f(x) = x^2 -3\)
d) \(f(x) = x^2 -5\)
Describe in your own words what you notice about the graphs of the functions. Given the function: \(f(x) = x^2 +c\), what happens as the value of \(c\) changes? Notice what happens at \(f(0)\).