The equation of function h is h(x) = 1/2(x-2)^2. The table shows some of the values of function m. (see attached image for the rest of the assignment)

A. -4

B. 4

C. no values

Step-by-step explanation:

When x increases by 2, m(x) increases by 1.  So m(x) is linear.  Pick two points to find the slope:

(3 − 2) / (10 − 8) = ½

Use point-slope form to write the equation:

m(x) − 2 = ½ (x − 8)

m(x) − 2 = ½ x − 4

m(x) = ½ x − 2

Part A

h(4) − m(16) = ½ (4 − 2)² − (½ (16) − 2)

h(4) − m(16) = 2 − 6

h(4) − m(16) = -4

Part B

h(0) − m(0) = ½ (0 − 2)² − (½ (0) − 2)

h(0) − m(0) = 2 − (-2)

h(0) − m(0) = 4

Part C

m(x) − h(x)

(½ x − 2) − ½ (x − 2)²

½ x − 2 − ½ (x² − 4x + 4)

½ x − 2 − ½ x² + 2x − 2

-½ x² + 2½ x − 4

Complete the square.

-½ (x² − 5x) − 4

-½ (x² − 5x + 25/4) − 4 + ½ (25/4)

-½ (x − 5/2)² − 7/8

This is always negative, so m(x) is always less than h(x).