Question

without graphing, determine whether the equation has a graph that is symmetric with respect to the x - axis, the y - axis, the origin, or none of these
y = x² + 10
choose the correct answer below. select all that apply.
a. x - axis
b. y - axis
c. origin
d. none of these

Explanation:

Step1: Test x-axis symmetry

Replace $y$ with $-y$:
$-y = x^2 + 10$ → $y = -x^2 - 10$
This is not equivalent to the original equation $y = x^2 + 10$, so no x-axis symmetry.

Step2: Test y-axis symmetry

Replace $x$ with $-x$:
$y = (-x)^2 + 10 = x^2 + 10$
This matches the original equation, so there is y-axis symmetry.

Step3: Test origin symmetry

Replace $x$ with $-x$ and $y$ with $-y$:
$-y = (-x)^2 + 10$ → $-y = x^2 + 10$ → $y = -x^2 - 10$
This is not equivalent to the original equation, so no origin symmetry.

Answer:

B. y-axis