Question

The area of square A is represented by f(x) = 4x² + 18. The area of square B, a larger square, is represented by g(x) = 6x² - 12. Formulate a function h(x) that represents how much larger square B is than square A.

a. h(x) = 2x² - 30
b. h(x) = 2x² + 30
c. h(x) = 2x² + 30x
d. h(x) = 2x² - 30x

Answer 1

To find out how much larger square B's area is than square A's, subtract the area function of square A from B's area function (h(x) = g(x) - f(x)) to get h(x) = 2x² - 30, making answer a correct.

Step-by-step explanation:

To determine the function h(x) that represents how much larger square B is than square A, we subtract the area function of square A from the area function of square B:

h(x) = g(x) - f(x)

h(x) = (6x² - 12) - (4x² + 18)

Simplify the equation by combining like terms:

h(x) = 6x² - 4x² - 12 - 18

h(x) = 2x² - 30

Therefore, the correct answer is a. h(x) = 2x² - 30, which indicates that the area of square B is 2x² - 30 square units larger than the area of square A.