Lesson 3 Well, What Do You Know? Develop Understanding

Jump Start

Match each of the following expressions to an equivalent expression or an area model for the expression:

  1. ___

  2. ___

  3. ___

  4. ___

  5. ___

  1. Area model with top left area x^2, top right area 7x, bottom left area -2x and bottom right area -14.
  2. Area model with top left area x^2, top right area x, bottom left area -3x and bottom right area -24. Top x 8 and side x-3

Learning Focus

Use patterns to efficiently graph quadratic functions from factored form.

How does the graph of a parabola relate to the equation of a quadratic function?

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

Open Up the Math: Launch, Explore, Discuss

This task is designed to help you to remember your work with parabolas from last year and to show what you know. For each of the following, find the indicated information.

1.

Given:

Parabola with vertex (-3,4) opening downwardsx–5–5–5y–5–5–5000

Type of function:

Vertex:

Line of Symmetry:

x-intercepts:

2.

Given:

Parabola with vertex (1,-4) x–5–5–5555y–5–5–5555101010000

Type of function:

Vertex:

Line of Symmetry:

-intercepts:

y-intercept:

3.

Given:

Parabola with x intercepts -3 and 2x–5–5–5555y–5–5–5555000

-intercepts:

-intercept:

line of symmetry:

vertex:

factored form of the equation:

4.

Given:

a blank 17 by 17 grid

Standard form of the equation:

-intercepts:

-intercept:

Line of symmetry:

5.

Given:

a blank 17 by 17 grid

Factored form of the equation:

-intercepts:

-intercept:

vertex:

line of symmetry:

6.

How do you find the -intercept of a quadratic equation in standard form? In factored form?

7.

How do you find the -intercepts of a quadratic equation in factored form?

8.

How do you find the line of symmetry of a parabola when the equation is in factored form?

9.

How do you find the vertex when you know the line of symmetry?

10.

How do you find the standard form equation of a quadratic equation in factored form?

Ready for More?

See if you can find these functions:

a.

Two different quadratic functions that have -intercepts and .

b.

Two different quadratic functions that have a -intercept of .

c.

Two different quadratic functions that have a line of symmetry of .

Takeaways

When a quadratic function is in factored form: ,

The -intercepts can be found by

The -intercept can be found by

The line of symmetry can be found by

The vertex can be found by

The parabola has a maximum if

Vocabulary

Lesson Summary

In this lesson, we reviewed how to graph quadratic functions in factored form and standard form. We learned to find the -intercepts from the factors, then find the line of symmetry between the -intercepts. Once we knew the line of symmetry, we could find the vertex. We observed several patterns that helped to make factored form an efficient way to graph quadratics.

Retrieval

1.

Fill in the table of values for each equation and then graph each function on the coordinate grid provided.

a.

b.

a blank coordinate planex–5–5–5555y–5–5–5555000

2.

How does the in the second equation change the graph in comparison to ?

3.

How does the in the third equation change the graph in comparison to ?

Write the equation of a line that is parallel to the given line and through the given point.

4.

point

5.

point