# Lesson 9 Lining Up Quadratics Solidify Understanding

## Learning Focus

Find patterns to efficiently graph quadratic functions from factored form.

What features of a parabola are highlighted in factored form? How can we use those features to graph a quadratic function?

How does the factored form of a quadratic equation relate to graphing a parabola?

## Open Up the Math: Launch, Explore, Discuss

Use technology to graph each function and find the vertex, the

### 1.

Line of symmetry:

Vertex:

x-intercepts:

y-intercept:

### 2.

Line of symmetry:

Vertex:

### 3.

Line of symmetry:

Vertex:

### 4.

Based on these examples, how can you use a quadratic function in factored form to:

#### a.

Find the line of symmetry of the parabola?

#### b.

Find the vertex of the parabola?

#### c.

Find the

#### d.

Find the

#### e.

Find the vertical stretch?

Now it’s time to try your strategy! Factor each of the functions, use the strategy that you found in problem 4 to find the vertex, intercepts, and line of symmetry, and graph each parabola without technology. Check your work with technology, and if your graph is wrong, go back and examine each step of your work to diagnose the problem.

### 5.

Factored form of the function:

Line of symmetry:

Vertex:

Vertical stretch:

### 6.

Factored form of the function:

Line of symmetry:

Vertex:

Vertical stretch:

### 7.

Factored form of the function:

Line of symmetry:

Vertex:

Vertical stretch:

### 8.

Factored form of the function:

Line of symmetry:

Vertex:

Vertical stretch:

## Ready for More?

Write three functions in factored form with a line of symmetry

## Takeaways

When a quadratic function is in factored form

The

The

The line of symmetry can be found by

The vertex can be found by

The vertical stretch and reflection can be found by

## Vocabulary

- factored form
**Bold**terms are new in this lesson.

## Lesson Summary

In this lesson, we learned to use the factored form of a quadratic equation to graph parabolas. We learned to find the

Multiply each expression, and write your answer as a trinomial.

### 1.

### 2.

### 3.

Given the vertex form of a quadratic function, identify the vertex, intercepts, and vertical stretch of the parabola.

### 4.

#### a.

Vertex:

#### b.

#### c.

#### d.

Stretch: