Question

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?

Answer 1

See below in bold.

Explanation:

a. The vertex is at (2, -1) in both functions.

b. Function A : Rate of increase = (change in y values)/ (change in x values)

= (0 - (-1)) / (3-2)

= 1.

c. Function B : Rate of change =

(0.5 - (-1)) / (3-2)

= 1.5.

d. Function B increases faster between x = 2 and x = 3.

Answer 2

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.

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

`(f(3)-f(2))/(x-x')`

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 =
`(2-1)/(3-2)`=1

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

=
`(f(3)-f(2))/(x-x')`

=
`(0.5+1)/(3-2)` [ 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.