Algebra II

Cards (10)

• 1
  Front

  What is the standard form of a quadratic function?

  Back

  f(x) = ax² + bx + c, where a ≠ 0.

• 2
  Front

  What is the imaginary unit i defined as?

  Back

  i is defined as the square root of -1, so i² = -1.

• 3
  Front

  What is a complex number?

  Back

  A number of the form a + bi, where a is the real part, b is the imaginary part, and i = √(-1).

• 4
  Front

  What is the Fundamental Theorem of Algebra regarding polynomial functions?

  Back

  Every polynomial of degree n ≥ 1 has exactly n roots (zeros) in the complex number system, counting multiplicity.

• 5
  Front

  What is a rational function?

  Back

  A function of the form f(x) = p(x)/q(x), where p(x) and q(x) are polynomials and q(x) ≠ 0.

• 6
  Front

  What is the inverse relationship between exponential and logarithmic functions?

  Back

  Logarithmic functions are the inverses of exponential functions: if f(x) = bˣ, then f⁻¹(x) = log_b(x).

• 7
  Front

  What is the formula for the sum of a finite geometric series?

  Back

  S_n = a₁(1 - rⁿ) / (1 - r), where a₁ is the first term, r is the common ratio, and r ≠ 1.

• 8
  Front

  What condition allows an infinite geometric series to converge, and what is its sum?

  Back

  An infinite geometric series converges when |r| < 1, and its sum is S = a₁ / (1 - r).

• 9
  Front

  What is the standard form equation of an ellipse centered at the origin?

  Back

  x²/a² + y²/b² = 1, where a and b are the lengths of the semi-major and semi-minor axes respectively.

• 10
  Front

  What distinguishes a hyperbola from an ellipse in its standard conic equation?

  Back

  A hyperbola has a minus sign between its terms: x²/a² - y²/b² = 1, whereas an ellipse uses a plus sign.