y=x^2-3 Is there symmetry? Yes, on the y-axis. How would I prove it? With an equation?
f(a) = (a)^2 - 3
= a^2 - 3
f(-a) = (-a)^2 - 3
= a^2 - 3
since f(a) = f)-a) for all values of a, there is symmetry about the y-axis (by definition)
Thanks!
To prove that a function has symmetry about the y-axis, we need to show that substituting -x for x in the equation results in an equivalent equation.
Let's substitute -x for x in the given equation, y = x^2 - 3:
y = (-x)^2 - 3
Simplifying, we have:
y = x^2 - 3
We can see that the equation obtained after substituting -x for x is the same as the original equation. Therefore, we can conclude that the function y = x^2 - 3 has symmetry about the y-axis.
This demonstrates how we can prove symmetry using algebraic manipulation.