that1chick
Rewrite y = 3x2 - 24x + 10 in general form.
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Mertsj
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General Form
You have already seen how to graph a quadratic function when it is in its standard form. Recall that the standard form of a quadratic function looks like: y=a(x-h)^2+k
But how do you graph a quadratic function when it is in its general form? The general form of a quadratic function looks like this: y=ax^2+bx+c
Mertsj
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So how does your author define general form?
that1chick
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h=x, k=y... the problem I'm having with this one is splitting the 3 in 3x^2...?
that1chick
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Its just asking to rewrite it not graph it... heres what I have so far:
Mertsj
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So you want h-k form?
that1chick
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-10 on both sides
Y-10=3x^2-24x
24/2=12 12^2=144
Y-10=3x^2-24x+144
that1chick
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Its in standard form, I want general form(:
Mertsj
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Let's write it like this:
|dw:1362857059987:dw|
Mertsj
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Now complete the square inside the parentheses
that1chick
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OH! gcf! of course!!:D
Mertsj
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|dw:1362857161791:dw|
that1chick
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Thank you(: I forgot to look for a gcf
Mertsj
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yw
that1chick
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Y-10=3x^2-24x+144
Now factor the GCF
y-10=3(x^2-8x+48)
y-10=3(x-4)(x+12)
+10 to both sides
Y=3(x-4)(x+12) +10
Right?
that1chick
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how did you get 16^^
that1chick
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Oh wait... I know
Mertsj
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No. You cannot add 48 to one side without adding it to the other side. Did you see in my example that I added 16 inside the parentheses to complete the square? But I was really adding 48 to the right side because there is a 3 outside the parentheses. So then I subtracted 48 so there would be a net change of 0. Of course I could have added 48 to the left side which would have accomplished the same purpose.
Mertsj
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16 is the number that completes the square for x^2+8x
that1chick
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1 sec..
that1chick
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Y-10=3x^2-24x
GCF
Y-10=3(x^2-8x)
Complete the square
8/2=4 4^2=16
y-10=3(x^2-8x-16)
Simplify
y-10=3(x-4)^2
+10 to both sides
y=3(x-4)^2 +10
Right?
that1chick
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and by simplify I mean find the binomial...(:
Mertsj
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So let's multiply out your result:
\[y=3(x-4)^2+10=3(x^2-8x+16)+10=3x^2-24x+48+10=\]
Mertsj
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\[3x^2-24x+58\]
Mertsj
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Is that the problem you started with?
Mertsj
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If it isn't, then what you have done is changed the original problem instead of keeping the original problem and expressing it in another form.
that1chick
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What am I doing wrong?
Mertsj
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When you add 48 to the right side, you then have 2 choices:
1. subtract 48 from the right side
2. Add 48 to the left side.
that1chick
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y-10=3x^2-24x
y-10=3x^2-24x+48
+48
y+38=3x^2-24x+48
that1chick
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y+38=3(x^2-8x+16)
y+38=3(x-4)^2
Right so far?
that1chick
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Ok I solved it out on paper(: thank you for helping me
Mertsj
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yes
Mertsj
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yw
that1chick
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24/2=12 12^2=144........
Mertsj
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That is true. Not sure it is very useful.
that1chick
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y-10=3x^2-24x+144
that1chick
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k, never mind