Hey guys, it's Jhelene from PreCal 30s blogging about a summary of today's class.
Let me refresh your minds and let's do a quick recap on what we've learned so far! We now know how to use two forms of quadratic functions:
standard form
f (x)= ax2+ bx + c
and vertex form
f (x)= a(x-h)2+k
Still keeping up? Okay, so today we had another quick quiz as a replacement for yesterday's ripped quizzes. (If you missed what happened, click here to read more!)
Lots of whispers filled the room as algetiles were shown on the Smart board. I myself haven't used those in quite a while so it was kind of interesting how this is going to play a role in quadratic functions. We were separated into our own groups and were given pattern activity worksheets. The first question seemed simple: "Is (x+3)2 =x2 + 9? Why or why not?"
Half the class said no and half said yes but I honestly was doubting my own answer. The answer actually was no, because it is not a perfect square.
From the response he got from the first question, Mr. P reviewed expanding binomials as well as how to fill in the boxes to make both sides of the equation equal. I will show you an example and how to solve it.
x2 + 12x +__ =(x +__ )2
Note that this equation is from the basic function: ax2+bx+c.
Now to solve for the left side, use the formula: c=(b/2)2. This means you take "b", which is 12, dividing it by 2 then squaring it. This makes "c" 36.
To solve for the right side, just take the "b" again, and simply divide it by two. Easy, right?
We moved on from the worksheet to the blue booklet to a new topic called Transformations of a Quadratic Function. When we are presented a quadratic function in the first form, we use a process called "completing the square" to convert it to second form and better examine its defining characteristics. Mr. P gave us steps on how to complete this process.
Example:
y= x2 - 2x + 3
Step 1:
x2 - 2x +3 = 0
Step 2:
x2 - 2x = (-3)
Step 3:
(-2/2)2 -> -1 -> 1
Note: Remember not to remove the "b" value in the equation. Ste 3 will only be added to equation, not replace "b".
Step 4:
x2 - 2x + 1x = (-3) +1
x2 - 2x + 1x = (-2)
(x-1)2 = (-2)
this is when you bring back the "c" to the left
(x-1)2 +2 = 0
And your final answer would be:
y= (x-1)2 + 2
Always remember that moving number from one side to the other side changes its sign!! Thanks for reading this- if you did- and I hope this recap of today's lesson helped you and good luck for the rest of the semester! :)
Let me refresh your minds and let's do a quick recap on what we've learned so far! We now know how to use two forms of quadratic functions:
standard form
f (x)= ax2+ bx + c
and vertex form
f (x)= a(x-h)2+k
Still keeping up? Okay, so today we had another quick quiz as a replacement for yesterday's ripped quizzes. (If you missed what happened, click here to read more!)
Lots of whispers filled the room as algetiles were shown on the Smart board. I myself haven't used those in quite a while so it was kind of interesting how this is going to play a role in quadratic functions. We were separated into our own groups and were given pattern activity worksheets. The first question seemed simple: "Is (x+3)2 =x2 + 9? Why or why not?"
Half the class said no and half said yes but I honestly was doubting my own answer. The answer actually was no, because it is not a perfect square.
From the response he got from the first question, Mr. P reviewed expanding binomials as well as how to fill in the boxes to make both sides of the equation equal. I will show you an example and how to solve it.
x2 + 12x +__ =(x +__ )2
Note that this equation is from the basic function: ax2+bx+c.
Now to solve for the left side, use the formula: c=(b/2)2. This means you take "b", which is 12, dividing it by 2 then squaring it. This makes "c" 36.
To solve for the right side, just take the "b" again, and simply divide it by two. Easy, right?
We moved on from the worksheet to the blue booklet to a new topic called Transformations of a Quadratic Function. When we are presented a quadratic function in the first form, we use a process called "completing the square" to convert it to second form and better examine its defining characteristics. Mr. P gave us steps on how to complete this process.
Example:
y= x2 - 2x + 3
Step 1:
x2 - 2x +3 = 0
Step 2:
x2 - 2x = (-3)
Step 3:
(-2/2)2 -> -1 -> 1
Note: Remember not to remove the "b" value in the equation. Ste 3 will only be added to equation, not replace "b".
Step 4:
x2 - 2x + 1x = (-3) +1
x2 - 2x + 1x = (-2)
(x-1)2 = (-2)
this is when you bring back the "c" to the left
(x-1)2 +2 = 0
And your final answer would be:
y= (x-1)2 + 2
Always remember that moving number from one side to the other side changes its sign!! Thanks for reading this- if you did- and I hope this recap of today's lesson helped you and good luck for the rest of the semester! :)
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