June 26, 2019

Chapters

The equation of a **quadratic function** is:

**y = ax² + bx +c **

Its **graph** is a **parabola**.

### Graphical Representation of the Parabola

A parabola can be built from these points:

### 1. Vertex

The **axis of symmetry** passes through the **vertex** of the parabola.

The equation of the **axis of symmetry** is:

### 2. x-intercepts

For the intercept with the x-axis, the **second coordinate** is always **zero**:

**ax² + bx +c = 0**

To find the x-intecepts, solve the resultant quadratic equation:

**Two intercept points: (x _{1}, 0) (x_{2}, 0) if b² − 4ac > 0 **

**One intercept point: (x _{1}, 0) if b² − 4ac = 0 **

**No intercept points if b² − 4ac < 0 **

### 3. y-intercept

For the intercept with the y-axis, the **first coordinate** is always **zero**:

**f(0) = a · 0² + b · 0 + c = c** (0, c)

## Example

Graph the quadratic function y = x² − 4x + 3.

## 1. Vertex

x_{v } = − (−4)/2 = 2 y_{v }= 2² − 4 · 2 + 3 = −1

V(2, −1)

## 2. x-intercepts

x² - 4x + 3 = 0

(3, 0) (1, 0)

## 3. y-intercept

(0, 3)