Regents Ultimate Regents Algebra 2

Question 1

A function is defined as f(x) = 3x² - 12x + 9. What are the zeros of this function?

Accepted Answer

x = 1 and x = 3

Answer

Factor out 3 to get 3(x² - 4x + 3) = 3(x - 1)(x - 3), so zeros are x = 1 and x = 3.

Question 2

The sequence 5, 8, 11, 14, ... is arithmetic. What is the 20th term?

Accepted Answer

62

Answer

Using aₙ = a₁ + (n-1)d: a₂₀ = 5 + (19)(3) = 5 + 57 = 62.

Question 3

Which inequality represents the solution to -4x + 7 > 19?

Accepted Answer

x < -3

Answer

Subtracting 7 gives -4x > 12; dividing by -4 (flip inequality) gives x < -3.

Question 4

If f(x) = 2x + 5 and g(x) = x², what is f(g(3))?

Accepted Answer

23

Answer

g(3) = 9, then f(9) = 2(9) + 5 = 23.

Question 5

What is the axis of symmetry of the parabola y = -2x² + 8x - 3?

Accepted Answer

x = 2

Answer

The axis of symmetry is x = -b/(2a) = -8/(2·(-2)) = -8/(-4) = 2.

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