Quadratic Function

A quadratic function is a type of polynomial function with the highest degree of 2. Its general form is:

$$f(x) = ax^2 + bx + c$$

Where:

• $$a$$ is the coefficient of the quadratic term,
• $$b$$ is the coefficient of the linear term, and
• $$c$$ is the constant term.

Graph of a Quadratic Function

The graph of a quadratic function is a parabola. The direction of the parabola (upward or downward) and its location on the coordinate plane depend on the value of $$a$$.

• If $$a > 0$$, the parabola opens upwards.
• If $$a < 0$$, the parabola opens downwards.

Vertex of a Quadratic Function

The vertex of a quadratic function is the highest or lowest point on the parabola. The vertex has coordinates $$(h, k)$$, where:

$$h = \frac{-b}{2a}$$

$$k = f(h)$$

Axis of Symmetry

The axis of symmetry is a vertical line that passes through the vertex of the parabola. Its equation is:

$$x = \frac{-b}{2a}$$

Study Guide

To study quadratic functions effectively, make sure to:

1. Understand the general form of a quadratic function.
2. Learn how to identify the coefficients $$a$$, $$b$$, and $$c$$ from the function.
3. Practice graphing quadratic functions and identifying the direction of the parabola.
4. Calculate the vertex and axis of symmetry for a given quadratic function.
5. Work on solving quadratic equations by factoring, completing the square, or using the quadratic formula.

It's also important to practice solving word problems involving quadratic functions to apply the concepts in real-world situations.

Hope this guide helps you understand quadratic functions better!