Standards Flashcards

If a polynomial P(x) has a root at x = -4, which factor must P(x) contain?

Answer: (x + 4)

If x = -4 is a root, then (x - (-4)) = (x + 4) is a factor by the Factor Theorem.

What is the distance between points (-1, 2) and (3, 5)?

Answer: 5

d = √((3-(-1))² + (5-2)²) = √(16 + 9) = √25 = 5.

Which transformation maps f(x) to f(x) + 3?

Answer: Vertical shift up 3

Adding a constant outside the function shifts the graph vertically upward by that amount.

Simplify: (x³)² / x⁴

Answer: x²

(x³)² = x⁶; then x⁶/x⁴ = x⁶⁻⁴ = x².

What is the sum of the interior angles of a hexagon?

Answer: 720°

Using (n-2)·180° with n=6: (6-2)·180 = 4·180 = 720°.

Which of the following best describes the end behavior of f(x) = -x³ + 2x?

Answer: As x→∞, f→-∞; as x→-∞, f→∞

The leading term -x³ dominates: for large positive x the value is large negative, and vice versa.

What is the midpoint of the segment with endpoints (0, 4) and (6, 10)?

Answer: (3, 7)

Midpoint = ((0+6)/2, (4+10)/2) = (3, 7).