Chapter 3 Vocabulary

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Across
  1. 3. The highest or lowest point on a parabola. It represents the exact turning point where the graph changes direction from increasing to decreasing (or vice versa.
  2. 4. A specific factoring pattern where a perfect square term is subtracted from another perfect square term. It always factors cleanly as: a^2 - b^2 = (a - b)(a + b).
  3. 11. The specific part of the quadratic formula found under the radical: b^2 - 4ac. It determines the number and type of solutions.
  4. 13. A non-linear function that can be written in the form y = ax^2 + bx + c, where "a" cannot equal 0. Its graph creates a smooth, U-shaped curve called a parabola.
  5. 15. Another name for the solutions to a quadratic equation. Graphically, the real roots are exactly the same values as the x-intercepts (also called zeros).
  6. 16. A central, vertical line that splits a parabola down the middle into two symmetrical halves. It always passes directly through the vertex.
  7. 17. A quadratic expression written as a product of two linear binomials, like y = a(x - p)(x - q).
Down
  1. 1. The foolproof algebraic tool used to find the solutions of any quadratic equation in standard form
  2. 2. A three-term expression created by squaring a single binomial. It takes the form a^2 + 2ab + b^2 and factors into identical binomial parts: (a + b)^2.
  3. 5. The lowest y-value on a parabola. It occurs at the vertex only when the parabola opens upward (when the leading coefficient a is positive.
  4. 6. A mathematical statement where a quadratic expression is set equal to a value (e.g. ax^2 + bx + c = 0).
  5. 7. The point(s) where the parabola crosses the horizontal x-axis. A quadratic function can have two, one, or zero real x-intercepts.
  6. 8. The single point where the parabola crosses the vertical y-axis. This occurs where x = 0
  7. 9. A organized layout for a quadratic expression written from highest degree to lowest: ax^2 + bx + c, where a, b, and c are constants.
  8. 10. The set of all possible outputs (y-values.
  9. 12. The set of all possible x-values(input values) of the function.
  10. 14. The highest y-value on a parabola. It occurs at the vertex only when the parabola opens downward (when the leading coefficient a is negative.