Question

determine whether the graph of the below equation is symmetric with respect to the y - axis, the x - axis, the origin, more than one of these, or none of these.
$y^2 = x^3 + 4$
select all that apply.
□ origin
□ y - axis
□ none of these
□ x - axis

Explanation:

Step1: Test x-axis symmetry

Replace $y$ with $-y$:
$(-y)^2 = x^3 + 4$
Simplify: $y^2 = x^3 + 4$ (matches original equation)

Step2: Test y-axis symmetry

Replace $x$ with $-x$:
$y^2 = (-x)^3 + 4$
Simplify: $y^2 = -x^3 + 4$ (does not match original)

Step3: Test origin symmetry

Replace $x$ with $-x$ and $y$ with $-y$:
$(-y)^2 = (-x)^3 + 4$
Simplify: $y^2 = -x^3 + 4$ (does not match original)

Answer:

x-axis