Lesson 2.3.1 How can I write it in graphing form?

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Lesson Objective:

We will review how to convert an equation for a parabola or a circle into graphing form by completing the square.

2-131.

With your team, decide on a strategy to find the vertex of the parabola

y=x ^2−2x−15

1. Find the x-intercepts of the parabola.

(5,0) (-3,0)

• Use the x-intercepts to find vertex.

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• Write the standard equation into graph form.

Plug x = 1 into the original equation to get y = -16

• Do you think if there are any better ways to find the vertex? If yes, please name the method.

Graph the equation or using completing squares.

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(5 -3)/2 = 1

Completing The Square

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2-132.

Tessa is at home struggling with her math homework. She missed class and does not understand completing the square. She is supposed to complete the square to rewrite y=x ^2+8x+10

in graphing form. Her friend Mara brought over her algebra tiles to help. She spread out the tiles shown below on the table, and said, “Now you need to build a square!”

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What is completing a square?

Group Activity 2-132

2-132.

1. Please use algebra tiles to complete the square.

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2-132.

B. Use algebra tiles or a rectangular area model to complete the square and rewrite the equation y=x^ 2+8x+10 in graphing form.

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Y + 6 = x^2 +8x +16

y = (x+4)^2 -6

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C. What is the vertex of the parabola?

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(-4, -6)

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D. Sketch a graph of the parabola.

Grouping Activity 2-133

2-133.

Help Tessa with a new problem. She needs to complete the square to write y=x^2 + 4x + 9

in graphing form. Use algebra tiles or an area model to help her figure out how to make this expression into a square. Does she have too few or too many unit tiles this time? Write her equation in graphing form, name the vertex, and sketch the graph.

y = (x+2)^2 +5

2-134. Tessa is stuck on another homework problem, and needs your team’s help again. She is supposed to sketch a quick graph of

x^ 2 + y^ 2 + 4x − 8y + 11=0. She is pretty sure that it is a circle, but she doesn't know how to get it into graphing form. She thinks she can use algebra tiles to figure it out, only this time she will need more kinds of tiles. She collected the tiles shown in the diagram below.

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Group Activity 2-134

x^ 2 + y^ 2 + 4x − 8y + 11=0.

1. With your team, figure out how to arrange the tiles to form two squares. This can be done using the Algebra tiles.
2. How many unit tiles are needed to complete the two squares?

20

• Write the equation in graph form.

(x+ 2) ^2 + (y-4)^2 = 9

Summary

• In order to convert the standard form of a parabola into the graph form, we can use “completing squares” to do it.

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• As for the standard form of a circle, we need to find two completing squares to convert it into its graph form.