Understanding Quadratic Functions

This page introduces the fundamental concepts of quadratic functions and provides guidance on how to graph them.

The document begins by defining a quadratic function as an equation where the highest exponent is 2. It then introduces the standard form of a quadratic equation: y = ax² + bx + c.

Definition: A quadratic function is represented by an equation in the form y = ax² + bx + c, where 'a', 'b', and 'c' are constants and 'a' ≠ 0.

Key components of a quadratic function are explained:

1. Parabola: The U-shaped graph that represents a quadratic function visually.
2. Vertex: The bottom or turning point of the parabola on the graph.
3. Axis of Symmetry: A vertical line that passes through the vertex, given by the formula x = -b/(2a).

Vocabulary: The vertex is the lowest or highest point of a parabola, depending on whether it opens upward or downward.

The document provides a step-by-step example of how to graph a quadratic function:

1. Identify the equation: y = 2x² + 4x - 3
2. Calculate the axis of symmetry: x = -4/(2(2)) = -1
3. Find the vertex by substituting x = -1 into the original equation
4. Calculate additional points by substituting other x-values
5. Plot the points and draw the parabola

Example: For the equation y = 2x² + 4x - 3, the axis of symmetry is x = -1, and the vertex is (-1, -4).

Highlight: When graphing a quadratic function, always start by finding the vertex and axis of symmetry, as these provide the foundation for sketching the parabola accurately.

The page concludes with a reminder to substitute the calculated x-value back into the original equation to find the corresponding y-value, which completes the ordered pair for graphing.

Quote: "Note: Substitute x with the number to get a point."

This comprehensive overview provides students with the essential knowledge and steps required to understand and graph quadratic functions, setting a strong foundation for more advanced topics in algebra and calculus.