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How can I write it in graphing form? Completing the Square
Presentation
•
Mathematics
•
8th - 10th Grade
•
Medium
Maria Cruz Farooqi
Used 4+ times
FREE Resource
14 Slides • 17 Questions
1
By MARIA FAROOQI
Learning Target: I will learn how to convert the equation of a parabola into graphing form by completing the square.
2
Poll
How are you feeling today?
3
Open Ended
Who is the most important person responsible for your academic success?
4
Multiple Choice
Find the x-intercepts of x2+8x+7=0 .
{5,8}
{1,7}
{−5,−8}
{−1,−7}
5
Make a rectangle with the tiles. How does the rectangle relate with the x-intercepts?
6
7
Multiple Choice
Find the x-intercepts of x2−2x−3=0 .
{−1,3}
{−8,−4}
{−5,6}
{6,−3}
8
Open Ended
Use the Zero Product Property to find the x-intercepts of y=x2+8x+10 . What went wrong? How could you work around this problem?
9
Open Ended
The previous problem used the equation y=x2+8x+10 . This function can be rewritten in vertex form as y=(x+4)2−6. Find the exact x-intercepts and vertex.
10
Jessica was at home struggling with her Algebra homework.
11
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.
12
13
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!"
"Ok," said Jessica, and she arranged her tiles on an equation mat shown right.
14
Poll
How many unit tiles do they need to complete this square?
10
12
14
16
15
"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."
16
"Oh, I see," said Anita. You started with y = x2 + 8x + 10, but now you can rewrite it as..."
17
“Thank you so much, Anita! Now I can easily write the function in graphing form,
18
Open Ended
How can you use your graphing calculator to verify that y=x2+8x+10 and y=(x+4)2+6 are equivalent functions?
19
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?
20
21
Multiple Choice
The graphing form (vertex form) of f(x)=x2+6x+7 is...
f(x)=(x+3)2+2
f(x)=(x+3)2−4
f(x)=(x+2)2−2
f(x)=(x+3)2−2
22
Multiple Choice
The vertex of f(x)=x2+6x+7 is...
(−2,−3)
(−3,−2)
(2,3)
(3,2)
23
Fill in the Blanks
The y-intercept of f(x)=x2+6x+7 is... (0, ?) (Just type the missing number.)
Type answer...
24
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?
25
26
Multiple Choice
The graphing form (vertex form) of f(x)=x2+4x+11 is...
f(x)=(x+4)2+2
f(x)=(x+2)2+7
f(x)=(x+4)2+3
f(x)=(x+2)2+4
27
Multiple Choice
The vertex of f(x)=x2+4x+11 is...
(4, 7)
(2,7)
(−4,7)
(−2,7)
28
Fill in the Blanks
The y-intercept of f(x)=x2+4x+11 is... (0, ?) (Just type the missing number.)
Type answer...
29
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
30
Multiple Choice
x2 + 6x + ____
31
Open Ended
Write about two things you learned today and one thing you already knew.
By MARIA FAROOQI
Learning Target: I will learn how to convert the equation of a parabola into graphing form by completing the square.
Show answer
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