Basic Concepts in Mathematics
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This document defines key concepts related to quadratic functions and their graphs: 1) A quadratic function is a second-degree polynomial function of the form f(x) = ax^2 + bx + c, where a cannot be 0. 2) The graph of a quadratic function is called a parabola, which has a vertex and may open upward or downward depending on the sign of a. 3) The axis of symmetry is the vertical line through the vertex that divides the parabola into two equal parts.
Basic Concepts in Mathematics
- 1. BASIC CONCEPTS IN MATHEMATICS GRAPH OF A QUADRATIC FUNCTION Prepared by: MS. REYBETH D. RACELIS, LPT
- 2. AXIS OF SYMMETRY The vertical line through the vertex that divides the parabola into two equal parts.
- 3. DIRECTION OF OPENING OF A PARABOLA Can be determined from the value of a in f(x) = ax² + bx + c. If a > 0, the parabola opens upward; if a < 0, the parabola opens downward.
- 4. DOMAIN OF A QUADRATIC FUNCTION The set of all possible values of x. Thus the domain is the set of all real numbers.
- 5. PARABOLA The graph of a quadratic function.
- 6. QUADRATIC FUNCTION A second-degree function of the form f(x) = ax² +bx + c where a, b, and c are real numbers and a ≠ 0. This is a function which describes a polynomial of degree 2.
- 7. RANGE OF A QUADRATIC FUNCTION Consists of all y greater than or equal to the y-coordinate of the vertex if the parabola opens upward. Consists of all y less than or equal to the y-coordinate of the vertex if the parabola opens downward.
- 8. VERTEX The turning point of the parabola or the lowest or highest point of the parabola. If the quadratic function is expressed in standard form y = a(x-h)² + k, the vertex is the point (h, k)