shivraj
f(x)=(-3x^2)+13x-11
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Hero
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What are you supposed to do with this? Graph it?
shivraj
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no
Hero
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What then? You haven't posted the directions.
zepp
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Find roots?
shivraj
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how to complete a square
shivraj
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yep
Hero
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Hint: Since y = f(x), rewrite it like this:
\(y = -3x^2 + 3x - 11\)
Next add 11 to both sides, then divide divide both sides by -3 to get:
\(\frac{y + 11}{-3} = x^2 - x\)
Now add \(\frac{1}{16}\) to both sides to get:
\(\frac{y + 11}{-3} + \frac{1}{16} = x^2 - x + \frac{1}{16}\)
Once you have finished reducing, you should have a new expression for y
shivraj
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is that the answer
shivraj
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?
Hero
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The final result I get comes out to
\(y = -\large\frac{48(x-\frac{1}{4}^2) - 3}{16} - 11\)
Hero
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But that hasn't been simplified
Romero
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How is that better than what he wrote originally?
Hero
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Because it said to complete the square
Hero
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Once you complete the square, you have to put it back in the form y =
Hero
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But let me fix one minor mistake
Hero
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\(y = -\large\frac{48(x-\frac{1}{4})^2 - 3}{16} - 11\)
shivraj
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ok
Hero
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Ideally, I think you would want to express that as just one fraction.
shivraj
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yes
Hero
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Well, I did most of the work for you. You can finish the rest.
Hero
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Also, you might want to change y back to f(x)
shivraj
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ok sure
goformit100
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yes
Hero
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\(f(x) = -\large3(x-\frac{1}{4})^2 - \frac{179}{16}\)
shivraj
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THANKS
shivraj
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hero
Hero
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Yeah, I see where I went wrong. I added 1/16 to both sides instead of adding 1/4 to both sides
shivraj
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ok