Quadratic Functions and Equations Lesson 1: Graphing Quadratic Functions.

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Presentation transcript:

Quadratic Functions and Equations Lesson 1: Graphing Quadratic Functions

The standard form of a quadratic function is f (x) = ax 2 + bx + c where a, b and c are real numbers and a  0. Its graph is called parabola. Every parabola is symmetrical about a line called the axis of symmetry x y Axis of symmetry f (x) = ax 2 + bx + c Vertex Characteristics of quadratic functions The y-intercept: c

When a > 0 the graph opens upward and the vertex is the minimum x y f(x) = ax 2 + bx + c a > 0 opens upward vertex minimum When a < 0 the graph opens downward and the vertex is the minimum x y f(x) = ax 2 + bx + c a < 0 opens downward vertex maximum The domain: All real numbers IR Exercise: Find the characteristics of the following quadratic function, the domain and its range. y = 2x 2 + 4x – 3