1. two different quadratic functions have graphs with the same vertex. which function graph increases faster between x=2 and x=3? a. what is the vertex of each function graph? b. what is the average rate of change in function a between x=2 and x=3? c. what is the average rate of change in function b between x=2 and x=3? d. which function graph increases faster between x=2 and x=3?

A). (2, -1)

B). Average rate of change of function A = 1

C). Average rate of change of function B = 1.5

D). Graph of function B increases faster than function A.

Step-by-step explanation:

A). vertex of the function A will be (2, -1)

and vertex of the function B will be same as function A, (2, -1)

B). Average rate of change in function A between x = 2 and x = 3 will be

Equation of the function A will be f(x) = (x - 2)²-(-1)

f(x) = (x - 2)² + 1

f(3) = (3 -2)² + 1

     = 1² + 1 = 2

f(2) = 0 + 1 = 1

Therefore, rate of change = =1

C). Average rate of change of function B will be

=

= [ from the given table]

= 1.5

D).Since rate of change of graph B is greater than graph A therefore, function B will increase faster than function A.