that answer wasn't the one I looked for. i didn't want to be mean so i reposted it. can you please help me! THANK YOU SO MUCH !!
describe the similarities and differences between y=x^2 and a power funtion with a even degree higher than two?
I don't have an answer different from the one you were given. If I could help more I would.
What answer are you looking for?
The answer did answer the question.
The answer gave similarities and differences.
yes, butit talks about odd powers... i am looking for the relationship between even powers.
See post:
http://www.jiskha.com/display.cgi?id=1297297572
Of course, I'll be happy to help you describe the similarities and differences between the functions y = x^2 and a power function with an even degree higher than two.
First, let's discuss the similarities. Both y = x^2 and a power function with an even degree higher than two are types of polynomial functions. They involve raising the variable x to a certain power, which determines the shape of the graph.
Now, let's move on to the differences. The primary difference lies in the degree of the power function. The function y = x^2 has a degree of 2, which means it's a quadratic function. On the other hand, a power function with an even degree higher than two would have a degree greater than 2, such as y = x^4 or y = x^6.
The degree of a polynomial function affects the shape and behavior of its graph. A quadratic function y = x^2 has a U-shaped graph called a parabola. It opens upwards if the coefficient of x^2 is positive and downwards if it's negative. The vertex of the parabola is at (0, 0), and it's symmetric about the y-axis.
In contrast, a power function with an even degree higher than two would have a graph that is generally more complex and can exhibit different shapes. For example, a function like y = x^4 would have a graph that resembles two parabolas facing each other, also known as a "W" shape. The specific shape would depend on the sign of the coefficient of x^4 and the additional terms in the function.
To summarize, the similarities between y = x^2 and a power function with an even degree higher than two include being polynomial functions involving raising x to a power. The primary difference lies in the degree of the function, resulting in different shapes and behavior of their graphs.