Equivalent quadratic expressions Vertex paths Use the dynamic figures below to follow the path that the vertex of a quadratic function makes as you change one or more of the parameters that define the function. Use the figure below, as well as the Product Form, Polynomial Form, and Vertex Form tools, to investigate various paths that are formed by the vertex when you change one or more parameters. Make conjectures about the shapes of the paths formed and check them by graphing a function g (use the input box in the lower part of the tool) that describes the path. Use algebraic expressions to explain, generalize, and prove phenomena you have noticed. f(x)=m(x-r)(x-s) change trace m= r= s= f(x)=ax2+bx+c change trace a= b= c=

Vertex Form Polynomial Form Product Form Reading information about a function Immunization against the common cold Numeric surprises Constructing functions Wage increase Partial pictures Examining value tables Families of functions Vertex paths Family and sub-families Parametric families Exercise 1 Exercise 2 Exercise 3 Exercise 4 Exercise 5 Exercise 6 Exercise 7 Exercise 8 Exercise 9 Exercise 10 Exercise 11 Exercise 12