SOLUTION: I need help with this problem: f(x)=-4x^2+ 4x-1 This is what the problem asks: a)use the quad formula to find zeros b)Find Max or min value c)sketch the graph This is wha

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I need help with this problem: f(x)=-4x^2+ 4x-1 This is what the problem asks: a)use the quad formula to find zeros b)Find Max or min value c)sketch the graph This is wha      Log On


   

Question 108951: I need help with this problem:
f(x)=-4x^2+ 4x-1
This is what the problem asks:
a)use the quad formula to find zeros
b)Find Max or min value
c)sketch the graph
This is what I have done so far:
-4+/- sqr rt(4^2-4(-4)(-1))/2(-4)
Note: This should be set up using the quad formula
This is what I came up with:
x= -4+/- sqrt(16-16)/ -8
Note: also set up in quad formula.
My problen is what to to with the 16s. If I subtract them that leaves Zero. I'm stuck here. I can look at the equation and tell it will be a max value but what are the zeros? Please help?
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
You are correct so far. The sqrt(16 - 16) is zero. If you replace it with zero in your equation
for x you get:
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x+=+%28-4%2B-0%29%2F-8+=+%28-4%29%2F%28-8%29+=+1%2F2
.
And you are further correct that this graph rises to a peak and then drops back down.
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This means that you only have one zero and it occurs when x is equal to 1%2F2. So the graph
just touches the x-axis at its peak and that "touching" is at the value x = 1%2F2.
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And at this point the maximum value is y = 0. The graph looks like this:
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graph%28300%2C300%2C-5%2C5%2C-10%2C2%2C-4x%5E2%2B4x-1%29
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You did everything correctly, but just didn't recognize how to interpret your answer.
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Hope this helps you to see how to view answers when the terms in the radical reduce to zero.
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