Answer:
Option (4)
Step-by-step explanation:
To solve this problem we will satisfy the polynomials given in the options with the input-output values given in the table.
Lets take a point (4, 40),
Option (1),
f(h) = h² + 4h + 80
40 = 4² + 4(4) + 80
40 = 16 + 16 + 80
40 = 112
False.
Therefore, table doesn't represent the polynomial given in option (1).
Option (2)
f(h) = 5h²- 5h + 13
40 = 5(4)² - 5(4) + 13
40 = 80 - 20 + 13
40 = 73
False.
Therefore, table doesn't represent the polynomial given in option (2).
Option (3)
f(h) = h³ + 50h² + 13
40 = 4³ + 50(4)²+ 13
40 = 64 + 800 + 13
40 = 873
False.
Therefore, table doesn't represent the polynomial given in option (3).
Option (4)
f(h) = 5h³- 50h²+ 13h
40 = 5(4)³ - 50(4)²+ 130(4)
40 = 320 - 800 + 520
40 = 840 - 800
40 = 40
True.
Therefore, given table represents this polynomial.
Option (4) will be the answer.
