How can I write it in graphing form? Completing the Square

How can I write it in graphing form? Completing the Square

By MARIA FAROOQI

​Learning Target: I will learn how to convert the equation of a parabola into graphing form by completing the square.

Poll

How are you feeling today?

Open Ended

Who is the most important person responsible for your academic success?

Multiple Choice

Find the x-intercepts of $$x^2+8x+7=0$$  .

• $$\left\{5,8\right\}$$  

• $$\left\{1,7\right\}$$  

• $$\left\{-5,-8\right\}$$  

• $$\left\{-1,-7\right\}$$  

​Make a rectangle with the tiles. How does the rectangle relate with the x-intercepts?

​

Can you make a rectangle?

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Multiple Choice

Find the x-intercepts of $$x^2-2x-3=0$$  .

• $$\left\{-1,3\right\}$$  

• $$\left\{-8,-4\right\}$$  

• $$\left\{-5,6\right\}$$  

• $$\left\{6,-3\right\}$$  

Open Ended

Use the Zero Product Property to find the x-intercepts of $$y=x^2+8x+10$$  . What went wrong? How could you work around this problem?

Open Ended

The previous problem used the equation $$y=x^2+8x+10$$  . This function can be rewritten in vertex form as $$y=\left(x+4\right)^2-6.$$  Find the exact x-intercepts and vertex.

COMPLETING THE SQUARE

Jessica was at home struggling with her Algebra homework.​

Jessica was at home struggling with her Algebra homework.  She had missed class and did not understand the new method called completing the square.  She was supposed to use it to change  to graphing form. 

​

Then her precocious younger sister, who was playing with algebra tiles, said, “Hey, I bet I know what they mean.”  Anita’s Algebra class had been using tiles to multiply and factor binomials.​

Explore the tiles on the following page.​

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Anita explained: "x² + 8x + 10 would look like this."

​

"Yes", said Jessica, " I am taking Algebra too, ​remember?

Anita continued, "And you have to make it into a square!"

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"Ok," said Jessica, ​and she arranged her tiles on an equation mat shown right.

Poll

How many unit tiles do they need to complete this square?

• $$10$$  

• $$12$$  

• $$14$$  

• $$16$$  

"Oh," ​said Jessica. " I need 16 small unit tiles to fill the corner!"

"But you only have 10​," Anita reminded her.

"Right, I only have ten," Jessica replied.

"Oh, I get it! ​To complete the square, I need to add six tiles to each side of the equation."

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​"Oh, I see," said Anita. You started with y = x² + 8x + 10, but now you can rewrite it as..."

​“Thank you so much, Anita!  Now I can easily write the function in graphing form,

Open Ended

How can you use your graphing calculator to verify that $$y=x^2+8x+10$$  and $$y=\left(x+4\right)^2+6$$  are equivalent functions?

Then state the vertex and y-intercept.​

​Write the function in graphing form.

​Need tiles? They are on the next slide.

​

​Did you figure out a shortcut yet?

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Multiple Choice

The graphing form (vertex form) of $$f\left(x\right)=x^2+6x+7$$  is...

• $$f\left(x\right)=\left(x+3\right)^2+2$$  

• $$f\left(x\right)=\left(x+3\right)^2-4$$  

• $$f\left(x\right)=\left(x+2\right)^2-2$$  

• $$f\left(x\right)=\left(x+3\right)^2-2$$  

Multiple Choice

The vertex of $$f\left(x\right)=x^2+6x+7$$  is...

• $$\left(-2,-3\right)$$  

• $$\left(-3,-2\right)$$  

• $$\left(2,3\right)$$  

• $$\left(3,2\right)$$  

Then state the vertex and y-intercept.​

​Write the function in graphing form.

​Need tiles? They are on the next slide.

​

​Did you figure out a shortcut yet?

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Multiple Choice

The graphing form (vertex form) of $$f\left(x\right)=x^2+4x+11$$  is...

•   $$f\left(x\right)=\left(x+4\right)^2+2$$  

•   $$f\left(x\right)=\left(x+2\right)^2+7$$  

•   $$f\left(x\right)=\left(x+4\right)^2+3$$  

•   $$f\left(x\right)=\left(x+2\right)^2+4$$  

Multiple Choice

The vertex of $$f\left(x\right)=x^2+4x+11$$  is...

•   $$\left(4,\ 7\right)$$  

• $$\left(2,7\right)$$   

• $$\left(-4,7\right)$$   

• $$\left(-2,7\right)$$   

Multiple Choice

Write the following quadratic expression in completed square form...

x² + 10x + 13

• (x + 5)² - 12

• (x + 5)² + 3

• (x + 5)² + 12

• (x + 5)² - 15

Multiple Choice

Complete the square.
x² + 6x + ____

• x² + 6x + 9
• x² + 6x - 36
• x² + 6x + 36
• x² + 6x - 9

Open Ended

Write about two things you learned today and one thing you already knew.