The word quadratic is derived from a Latin word, * "quadratum", *which means

**square.**As you guessed, any equation that has the degree of

**"2"**is a quadratic equation. It is usually in the form of , where a, b, and c are constants. Let's analyze some equations, we have three equations and you need to identify which equations are quadratic and which not(with a reason).

Take your time and find which equation/equations are quadratic or not. Here is the answer, the quadratic equations are on point number 2, and point number 4. The first equation contains but it isn't a quadratic equation because it contains a higher power which is , hence the degree of this equation is **"4"** not **"2". **In the case of the third equation, the degree is "1" because it only has one variable whose power is one. Last but not least, the fifth equation has a problem. You can subtract both and you will be left with which is not a quadratic equation.

Let's draw a graph of a simple quadratic equation. Here is a quadratic equation, , now let's draw a graph.

Does this graph look familiar with any shape to you? Yes! You are correct! It does look like a parabola. Can we conclude that all quadratic graphs look like a parabola? The answer is yes! Since the graph is a parabola, we will be applying all the rules and understandings of a parabola to it such as vertices, axis of symmetry, etc.

## 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**:

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

**Two intercept points: **

**One intercept point: **

**No intercept points if **

### 3. y-intercept

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

## Example

Graph the quadratic function .

### 1. Vertex

### 2. x-intercepts

### 3. y-intercept

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