Algebra

For each equation, determine whether its graph is symmetric with respect to the -axis, the -axis, and the origin.

4y^4+24x^2=28 and y=1/x^2+5

Check all symmetries that apply

x-axis,y-axis,origin or non of the above.

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  1. You need parentheses for the 2nd equation.

    Is this,
    y = 1/(x^2 + 5)

    Or,
    y = 1/(x^2) + 5

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  2. Sorry y=1/(x^2+5)

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  3. 4y^4 + 24x^2 = 28

    Symmetric to x-axis if an equivalent equation is obtained when y is replaced by -y.

    4y^4 + 24x^2 = 28
    4(-y)^4 + 24x^2 = 28
    4y^4 + 24x^2 = 28

    Since, the two equations are equivalent, the graph is symmetric to the x-axis.

    Symmetric to y-axis if an equivalent equation is obtained when x is replaced by -x.

    4y^4 + 24x^2 = 28
    4y^4 + 24(-x)^2 = 28
    4y^4 + 24x^2 = 28

    Since, the two equations are equivalent, the graph is symmetric
    to the y-axis.

    Symmetric to the origin if an equivalent equation is obtained when x is replaced by -x and y is replaced by -y.

    4y^4 + 24x^2 = 28
    4(-y)^4 + 24(-x)^2 = 28
    4y^4 + 24x^2 = 28

    Since, the two equations are equivalent, the graph is symmetric
    to the origin.

    I'll leave the 2nd equation for you to try.

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  4. I get that the second equation x-axis. Is that right?

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  5. Symmetric to y-axis if an equivalent equation is obtained when x is replaced by -x.

    It is symmetric to the y-axis, not x-axis.

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