Mr. Kone Math Hub · Review sheet

Solving Quadratic Equations

Unit 11: Quadratic Functions · AI-A.REI.4, AI-A.SSE.3

Algebra I Regents

Notes

Choose a method. If there is no x term, isolate and square-root. If it factors nicely, factor. Otherwise use x = (−b ± √(b² − 4ac))/(2a). The discriminant b² − 4ac tells you how many real roots.

Vocabulary

  • discriminant: b² − 4ac; determines the number of real solutions of a quadratic.

Practice (no calculator unless marked)

  1. When completing the square for x² − 18x + 77 = 0, which equation is a correct step in this process?
    • A. (x − 9)² = 4
    • B. (x − 3)² = 2
    • C. x = ±13
    • D. x − 9 = ±9
  2. The zeros of the function f(x) = x(x − 5)(3x + 6) are
    • A. 0, −5, and 2
    • B. 0, 5, and −2
    • C. −5 and 2, only
    • D. 5 and −2, only
  3. When completing the square for x² − 18x + 77 = 0, which equation is a correct step in this process?
    • A. (x − 9)² = 4
    • B. (x − 3)² = 2
    • C. x = ±13
    • D. x − 9 = ±9
  4. The zeros of the function f(x) = x(x − 5)(3x + 6) are
    • A. 0, −5, and 2
    • B. 0, 5, and −2
    • C. −5 and 2, only
    • D. 5 and −2, only
  5. When completing the square for x² − 18x + 77 = 0, which equation is a correct step in this process?
    • A. (x − 9)² = 4
    • B. (x − 3)² = 2
    • C. x = ±13
    • D. x − 9 = ±9
  6. The zeros of the function f(x) = x(x − 5)(3x + 6) are
    • A. 0, −5, and 2
    • B. 0, 5, and −2
    • C. −5 and 2, only
    • D. 5 and −2, only
  7. When completing the square for x² − 18x + 77 = 0, which equation is a correct step in this process?
    • A. (x − 9)² = 4
    • B. (x − 3)² = 2
    • C. x = ±13
    • D. x − 9 = ±9
  8. The zeros of the function f(x) = x(x − 5)(3x + 6) are
    • A. 0, −5, and 2
    • B. 0, 5, and −2
    • C. −5 and 2, only
    • D. 5 and −2, only