Understanding the Quadratic Function

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Learning Objective

At the end of the lesson you will be able to identify, analyse and graph quadratic functions, and solve practical tasks involving their properties.

What do you already know about quadratic functions?

What Is a Quadratic Function?

A quadratic function is a function of the form y = ax² + bx + c, where a ≠ 0. Its graph forms a parabola.

Key Elements of the Graph

The parabola has a vertex (maximum or minimum point), an axis of symmetry, and can open upwards or downwards depending on the coefficient a.

Vertex and Axis of Symmetry

The vertex is given by x = -b/(2a). The axis of symmetry is the vertical line passing through the vertex.

Effects of Coefficients

Changing a, b, or c alters the graph's shape and position. 'a' affects opening direction; 'b' shifts the vertex; 'c' moves the graph up or down.

Quadratic Function or Not?

1. y = 3x² - 5x + 2 2. y = 2x + 7 3. y = -x² 4. y = x³ Identify which ones are quadratic. Discuss your choices.

Which are quadratic?

1. Quadratic 2. Not quadratic 3. Quadratic 4. Not quadratic

Answers

Practice: Graph a Quadratic Function

Plot the function y = x² - 4x + 3. Identify the vertex, axis of symmetry, and y-intercept on your graph.

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