SOLUTION: Determine whether the graph of y=4x^2+1 is symmetric with respect to the x-axis, y-axis, and/or origin.

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Question 672886: Determine whether the graph of y=4x^2+1 is symmetric with respect to the x-axis, y-axis, and/or origin.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y=4x%5E2%2B1+
we need to check if f%28-x%29+=+-f%28x%29, if yes than a function is symmetric with respect to the origin
first find -y:
-y=-%284x%5E2%2B1%29
-y=-4x%5E2-1
now f%28-x%29
y=4%28-x%29%5E2%2B1+
y=4x%5E2%2B1+
so, f%28-x%29+%3C%3E+-f%28x%29 ...a function is not symmetric with respect to the origin



A graph is said to be symmetric about the x-axis if whenever (a,b) is on the graph then so is (a,-b)
as you can see from a graph, there is no point such as a%2C-b because the graph is above x-axis
see it on a graph

A graph is said to be symmetric about the y-axis if whenever (a,b) is on the graph then so is (-a,b)

(-a,b) is (-1,5), there is (1,5)


so, the graph of y=4x%5E2%2B1 is symmetric with respect to the y-axis