Question 1190465: Complete the square to write the following quadratic functions in vertex form. Use algebra tiles to illustrate and annotate each step of the completing the square process and include pictures here. You can use sentences to describe why the pictures and process makes sense.
y= -x^2 + 10x + 3
I already know that it can be presented as y = -(x-5)^2 - 22, but I got to that algebraically using equations. Could you help get to the solution using algebra tiles?
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52779)   (Show Source):
You can put this solution on YOUR website! .
Complete the square to write the following quadratic functions in vertex form.
Use algebra tiles to illustrate and annotate each step of the completing the square process
and include pictures here. You can use sentences to describe why the pictures and process makes sense.
y= -x^2 + 10x + 3
I already know that it can be presented as y = -(x-5)^2 - 22, but I got to that algebraically using equations.
Could you help get to the solution using algebra tiles?
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What " you already know " and what is written in your post, is not correct.
The correct answer is THIS: -x^2 + 10x + 3 = -(x-5)^2 + 28.
Step by step algebra transformations are as follows :
-x^2 + 10x + 3 = -(x^2 -10x) + 3 = -(x^2 - 10x + 25) + 25 + 3 = -(x-5)^2 + 28. ANSWER
CHECK with my formula. Take x = 0. You will get
-x^2 + 10x + 3 = -0^2 + 10*0 + 3 = 3 for the left side,
and -(0-5)^2 + 28 = -5^2 + 28 = -25 + 28 = 3 for the right side. ! correct !
Solved.
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To learn completing the square method, look into the lesson
- HOW TO complete the square - Learning by examples
in this site.
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I have no idea what is algebra tiles, never saw it and never kept them in my hands (thanks to god).
But you may request and find some videos in YouTube, for example, this one
https://www.youtube.com/watch?v=TyWLzx9UaDA
(and, probably, tens others similar videos).
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! My "algebra tiles" were repossessed for non-payment.
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My 1st algebra class was in 1954 or 1955.
This is the first time I've heard of "algebra tiles."
What about algebra shower curtains? Can I use those?
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