Question

Landon is a maintenance worker at an amusement park. He stands atop a raised platform of the park's most popular

roller coaster. At the start of Landon's inspection, the lead car is located 32 feet directly above him. The car races past
Landon's line of sight at x = 4 feet and again at x = 8 feet. Which function models this situation, the equation or the table?
Explain your answer.
f(x) = x3 - 11x2 + 20x + 32

Answer 1

For both functions, the lead roller coaster car starts at an initial height of 32 feet. This is the point (0,32), directly above Landon.

The car races past Landon’s field of vision (y = 0) after it moves a horizontal distance of 4 feet and then 8 feet with respect to the starting point. So, the correct function will have x-intercepts of 4 and 8.

Begin by checking the equation. Rewrite the equation in factored form:

f(x) = x3 − 11x2 + 20x + 32

= (x + 1)(x2 − 12x + 32)

= (x + 1)(x − 4)(x − 8)

The equation has x-intercepts of 4 and 8.

But the table only has one x-intercept, located at (4,0). The point (8,160) is well out of Landon’s line of sight.

So, the equation fits the situation, but the table doesn’t.

Answer 2

the equation fits the situation, but the table doesn’t.

Explanation:

For both functions, the lead roller coaster car starts at an initial height of 32 feet. This is the point (0,32), directly above Landon.

The car races past Landon’s field of vision (y = 0) after it moves a horizontal distance of 4 feet and then 8 feet with respect to the starting point. So, the correct function will have x-intercepts of 4 and 8.

Begin by checking the equation. Rewrite the equation in factored form:

f(x) =
`x^(3)` − 11
`x^(2)` + 20x + 32

= (x + 1)(
`x^(2)` − 12x + 32)

= (x + 1)(x − 4)(x − 8)

The equation has x-intercepts of 4 and 8.

But the table only has one x-intercept, located at (4,0). The point (8,160) is well out of Landon’s line of sight.

So, the equation fits the situation, but the table doesn’t.