CPM Math 2.2.4: 2-147

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jmyonemura

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When I tried to solve the problem, I tried to square everything inside the parentheses then multiply 2. As a result, I got y=2x^2+6, but the correct answer is y = 2x2 − 4x + 6

What am I doing wrong? Help would be greatly appreciated. Homework Help is hyperlinked to the appropiate problem webpage.
2-147. Sketch the graph of y = 2(x − 1)2 + 4. Homework Help ✎
  • Now rewrite the equation y = 2(x − 1)2 + 4 without parentheses. Remember the Order of Operations!
  • What would the difference be between the graphs of the two equations above? This is sort of a trick question, but explain your reasoning.
  • What is the parent function of y = 2(x − 1)2 + 4?
  • What is the parent function of y = 2x2 − 4x + 6?
 
jmyonemura said:
When I tried to solve the problem, I tried to square everything inside the parentheses then multiply 2. As a result, I got y=2x^2+6, but the correct answer is y = 2x2 − 4x + 6

What am I doing wrong? Help would be greatly appreciated. Homework Help is hyperlinked to the appropiate problem webpage.
2-147. Sketch the graph of y = 2(x − 1)2 + 4. Homework Help ✎
  • Now rewrite the equation y = 2(x − 1)2 + 4 without parentheses. Remember the Order of Operations!
  • What would the difference be between the graphs of the two equations above? This is sort of a trick question, but explain your reasoning.
  • What is the parent function of y = 2(x − 1)2 + 4?
  • What is the parent function of y = 2x2 − 4x + 6?
Click to expand...
When you tried to square everything inside the parentheses - what did you get?


y = 2(x − 1)2 + 4

y = 2[(x − 1)2 ] + 4 ........................ I added those brackets just for clarity later

Next you used the expansion

(a - b)2 = a2 - 2ab + b2

and you got (x - 1)2 = x2 - 2x + 12

Thus you got

y = 2[?? ] + 4

What did you have for [?? ] ?


 
jmyonemura said:
When I tried to solve the problem, I tried to square everything inside the parentheses then multiply 2. As a result, I got y=2x^2+6, but the correct answer is y = 2x2 − 4x + 6

What am I doing wrong? Help would be greatly appreciated. Homework Help is hyperlinked to the appropiate problem webpage.
2-147. Sketch the graph of y = 2(x − 1)2 + 4. Homework Help ✎
  • Now rewrite the equation y = 2(x − 1)2 + 4 without parentheses. Remember the Order of Operations!
  • What would the difference be between the graphs of the two equations above? This is sort of a trick question, but explain your reasoning.
  • What is the parent function of y = 2(x − 1)2 + 4?
  • What is the parent function of y = 2x2 − 4x + 6?
Click to expand...
"I tried to square everything inside the brackets" is completely wrong.

\(\displaystyle (a + b)^2 \equiv (a + b)(a + b) \equiv a(a + b) + b(a + b) = WHAT?\)
 
JeffM said:
"I tried to square everything inside the brackets" is completely wrong.

\(\displaystyle (a + b)^2 \equiv (a + b)(a + b) \equiv a(a + b) + b(a + b) = WHAT?\)
Click to expand...
Continue by distributing the a and b and collecting like terms.
 
jmyonemura said:
When I tried to solve the problem, I tried to square everything inside the parentheses then multiply 2. As a result, I got y=2x^2+6, but the correct answer is y = 2x2 − 4x + 6

What am I doing wrong? Help would be greatly appreciated. Homework Help is hyperlinked to the appropiate problem webpage.
2-147. Sketch the graph of y = 2(x − 1)2 + 4. Homework Help ✎
  • Now rewrite the equation y = 2(x − 1)2 + 4 without parentheses. Remember the Order of Operations!
  • What would the difference be between the graphs of the two equations above? This is sort of a trick question, but explain your reasoning.
  • What is the parent function of y = 2(x − 1)2 + 4?
  • What is the parent function of y = 2x2 − 4x + 6?
Click to expand...
You are saying that (x-1)2 = x2 + 1. But wouldn't you get the same starting with (x+1)2 ? That is (x+1)2 = x2 + 1 as well.

But what is that saying?? It says that if you start with any value for x (yes, x is a place holder for numbers!) and you either add 1 or subtract 1 and then square the result you get the same answer. This would mean that 16 = 42 = (5-1)2 = (5+1)2 = 62= 36
 
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