SOLUTION: Given the equation x+4y^2 =16 a) find the intercepts B)Is the graph symmetric with the x or y axis or both. What are the features that determine the symmetries. C) Graph the Eq

Question 1063585: Given the equation x+4y^2 =16
a) find the intercepts
B)Is the graph symmetric with the x or y axis or both. What are the features that determine the symmetries.
C) Graph the Equation. Find three additional points besides the intercepts.

Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!

Intercepts: (0,2), (0,-2), (16,0).

x is a quadratic in terms of y; the y is squared. The coefficient in x=-4(y+2)(y-2) or x=-4y^2+16 on the leading term is negative. Parabola opens to the left; symmetry axis is parallel to the horizontal axis.

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4y^2=-x+16
y^2=-x/4+4
y=0+- sqrt(-x/4+4)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Given the equation x+4y^2 =16
a) find the intercepts
If x = 0, y = +2 or x = -2
y-int's:: (0,2) and (0,-2)
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If y = 0, x = 16
x-int:: (16,0)
B)Is the graph symmetric with the x or y axis or both. What are the features that determine the symmetries.
f(x) = +-sqrt[16-x]
f(-x) = +-sqrt[16+x]
-f(-x) = +-sqrt[16+x]
Since f(-x) = -f(-x) you have origin symmetry
Since f(x) # -f(x) you do not have y-axis symmetry
It appears there is x-axis symmetry.
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Graph::

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C) Graph the Equation. Find three additional points besides the intercepts.
I'll leave that to you.
Cheers,
Stan H.
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