### Vertex Form of a Quadratic Equation

Probably one of the best applications of the method of completing the square is using it to rewrite a quadratic function in vertex form. The vertex form of a quadratic function is

This form is very useful for graphing because it gives the vertex of the parabola explicitly. The vertex is at the point .

It is also simple to find the intercepts from the vertex form: just set and take the square root of both sides of the resulting equation.

To find the intercept, set and simplify.

#### Finding the Vertex and Intercepts of Parabolas

Find the vertex, the intercepts and the intercept of the following parabolas:

a)

Vertex: (1, 2)

To find the intercepts,

The solutions are not real so there are **no** **intercepts.**

To find the intercept,

b)

To find the intercepts,

To find the intercept,

To graph a parabola, we only need to know the following information:

- the vertex
- the intercepts
- the intercept
- whether the parabola turns up or down (remember that it turns up if and down if )

#### Graphing Parabolas

1. Graph the parabola given by the function .

To find the intercepts,

To find the intercept,

And since , the parabola **turns up.**

Graph all the points and connect them with a smooth curve:

2. Graph the parabola given by the function .

To find the intercepts,

Note: there is only one intercept, indicating that the vertex is located at this point, (2, 0).

To find the intercept,

Since , the parabola **turns down.**

Graph all the points and connect them with a smooth curve:

### Example

#### Example 1

Graph the parabola given by the function .

To find the intercepts,

The intercepts are and .

To find the intercept,

Since , the parabola **turns up.**

Graph all the points and connect them with a smooth curve:

### Review

Rewrite each quadratic function in vertex form.

For each parabola, find the vertex; the and intercepts; and if it turns up or down. Then graph the parabola.

### Review (Answers)

To view the Review answers, open this PDF file and look for section 10.7.

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