SOLUTION: How do you state this in standard form and how is it graphed? I am trying to figure out lines of symmetry, domain, and range. 16x squared + 4y squared = 25. thanks! Zach

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: How do you state this in standard form and how is it graphed? I am trying to figure out lines of symmetry, domain, and range. 16x squared + 4y squared = 25. thanks! Zach      Log On


   

Question 438558: How do you state this in standard form and how is it graphed? I am trying to figure out lines of symmetry, domain, and range.
16x squared + 4y squared = 25.
thanks!
Zach
Found 2 solutions by stanbon, robertb:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How do you state this in standard form and how is it graphed? I am trying to figure out lines of symmetry, domain, and range.
16x squared + 4y squared = 25.
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16x^2+4y = 25
y = -4x^2+(25/4)
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16x^2 = -4y+25
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16x^2 = -4(y-(25/4))
(x-0) ^2 = (-1/4)(y-(25/4))
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Vertex at (0,25/4)
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Axis symmetry: x = 0
Domain: All Real numbers.
Range: The parabola opens downward from (0,25/4)
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Range: y<= 25/4
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Graph:
graph%28400%2C300%2C-10%2C10%2C-20%2C10%2C-4x%5E2%2B%2825%2F4%29%29
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Cheers,
Stan H.
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Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Hmm..."16x squared + 4y squared = 25"
That's an ellipse, 16x%5E2+%2B+4y%5E2+=+25
<==> x%5E2%2F%2825%2F16%29+%2B+y%5E2%2F%2825%2F4%29+=+1 in standard form.
There are two lines of symmetry,namely x = 0 and y = 0.
The domain can be gotten from the minor axis, which is along the x-axis:
sqrt%2825%2F16%29+=+5%2F4. Hence the domain is [-5/4, 5/4].
The range can be gotten from the major axis, which is along the y-axis:
sqrt%2825%2F4%29+=+5%2F2. Hence the range is [-5/2, 5/2].