Answer:
Step-by-step explanation:
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).
