Equivalent quadratic expressions Numeric surprises The three series of equalities below present two different calculations leading to the same result: 0*2=1²-1 1*3=2²-1 2*4=3²-1 3*5=4²-1 ... 0*1=(1²-1)/4 1*2=(3²-1)/4 2*3=(5²-1)/4 3*4=(7²-1)/4 ... 0²+1²=(1²+1)/2 1²+2²=(3²+1)/2 2²+3²=(5²+1)/2 3²+4²=(7²+1)/2 ... Formulate the three phenomena using six correspondence rules. Do the correspondence rules help you explain the "surprises"? Invent other series of numerical equalities that show similar phenomena.

Vertex Form Polynomial Form Product Form Reading information about functions 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