Lesson 10 I’ve Got a Fill-in Practice Understanding

Learning Focus

Choose the most efficient form of a quadratic function.

Become efficient and accurate in converting from one quadratic form to another.

Become efficient and accurate in identifying features of the graph of quadratic functions from a given form.

What information do we get from each form of a quadratic equation, and which form is best for a particular purpose?

Technology guidance for today’s lesson:

Find the Coordinates of the Vertex from a Table: Casio ClassPad Casio fx-9750GIII
Verify Different Forms of the Same Expression: Casio ClassPad Casio fx-9750GIII

Open Up the Math: Launch, Explore, Discuss

For each problem below, you are given a piece of information that tells you a lot. Use what you know about that information to fill in the rest.

1.

You get this:	Fill in this:
$y = x^{2} - x - 12$	Factored form of the equation:
$y = x^{2} - x - 12$	Graph of the equation:

2.

You get this:	Fill in this:
$y = x^{2} - 6 x + 3$	Vertex form of the equation:
$y = x^{2} - 6 x + 3$	Graph of the equation:

3.

You get this:	Fill in this:
	Vertex form of the equation:
	Standard form of the equation:

4.

You get this:	Fill in this:
	Factored form of the equation:
	Standard form of the equation:

5.

You get this:	Fill in this:
$y = - x^{2} - 6 x + 16$	Either form of the equation other than standard form:
	Vertex of the parabola:
	$x$ -intercepts and $y$ -intercept:

6.

You get this:	Fill in this:
$y = 2 x^{2} + 12 x + 13$	Either form of the equation other than standard form:
	Vertex of the parabola:
	$x$ -intercepts and $y$ -intercept:

7.

You get this:	Fill in this:
$y = - 2 x^{2} + 14 x + 60$	Either form of the equation other than standard form:
	Vertex of the parabola:
	$x$ -intercepts and $y$ -intercept:

Ready for More?

Play the I’ve Got A Fill-in game. You need four people who are finished with the task to play. The first person starts by writing a function in factored form. Don’t make the numbers too messy. The game continues with the next person filling in block 2, the third person completing block 3, and so on. Each time the next person starts completing their block, the other people in the group should be checking the previous work. If you can correct an error, you get extra brownie points. Have fun!

1: Write a quadratic function in factored form.	2: Find $x$ -intercepts, the $y$ -intercept, the vertex, and the line of symmetry.

3: Write the function in standard form.	4: Graph the function.

Takeaways

It is easier to convert to vertex form when:

Vertex form is efficient for finding:

It is easier to convert to factored form when:

Factored form is efficient for finding:

Standard form is efficient for finding:

Helpful hints for avoiding algebraic errors in factoring, completing the square, or changing to standard form:

Lesson Summary

In this lesson, we learned to make strategic choices about the most efficient form for working with the graph of a quadratic function. We considered which form is most efficient for obtaining features like the vertex, $x$ -intercepts, $y$ -intercept, the vertical stretch, and reflection. We also considered which form will be most efficient to convert from standard form, knowing that some trinomials do not factor easily and some trinomials make completing the square complicated.

Retrieval

Rewrite each of the quadratic equations in vertex form.

1.

$f (x) = x^{2} + 12 x - 13$

2.

$g (x) = x^{2} - 8 x + 42$

3.

$h (x) = 2 x^{2} + 8 x + 15$

Write each of the following in factored form.

4.

$x^{2} + 15 x + 56$

5.

$x^{2} - 5 x - 24$