SOLUTION: how do you identify the vertex, focus, and directrix of the parabola y=x^2+4x+3 And graph it.

Algebra ->  Trigonometry-basics -> SOLUTION: how do you identify the vertex, focus, and directrix of the parabola y=x^2+4x+3 And graph it.      Log On


   

Question 736234: how do you identify the vertex, focus, and directrix of the parabola
y=x^2+4x+3
And graph it.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
how do you identify the vertex, focus, and directrix of the parabola
y=x^2+4x+3
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graph%28400%2C400%2C-10%2C10%2C-10%2C10%2Cx%5E2%2B4x%2B3%29
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Complete the square:
x^2+4x+? = y-3+?
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x^2+4x+4 = y-3+4
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(x+2)^2 = (y+1)
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Form:
(x-h)^2 = 4p(y-k)
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Vertex: (-2,-1)
4p = 1
p = 1/4
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Directrix is 1/4 below the vertex:
y = -5/4
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Focus is 1/4 above the vertex:
Focus: (-2,-3/4)
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Cheers,
Stan H.
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