The equation y=10/x^2 represents a hyperbola with a vertical asymptote at x=0. The value of y increases as x approaches 0 from the positive and negative sides.
To graph this equation, you can create a table of values by choosing different values for x and then calculating the corresponding values of y using the equation. Then, plot these points on a graph and connect them with a smooth curve. Remember to include the vertical asymptote at x=0.
The domain of this equation is all real numbers except for 0, since division by 0 is undefined. The range is all real numbers greater than 0, since the value of y is always positive.
To find the x-intercept, set y=0 and solve for x. In this case, there is no x-intercept since the equation has a vertical asymptote at x=0. To find the y-intercept, set x=0 and solve for y. In this case, the y-intercept is (0, 10).
The equation has two asymptotes: a vertical asymptote at x=0 and a horizontal asymptote at y=0. The graph of the equation approaches these asymptotes but never touches them.