The equation y=1+x+x^3 is a polynomial equation with three terms. The first term is a constant, the second term is a linear term, and the third term is a cubic term.
The variable y represents the output or dependent variable, while the variable x represents the input or independent variable. In this equation, x is raised to the powers of 1 and 3, which means it is a quadratic function.
The constant term, 1, is the y-intercept of the graph of this equation. It represents the value of y when x is equal to 0. In other words, it is the starting point of the graph.
The graph of y=1+x+x^3 is a cubic function, which means it has a distinctive "S" shape. This is different from linear and quadratic functions, which have a straight line and a parabola shape, respectively.
The equation y=1+x+x^3 can be used to model various real-life phenomena, such as population growth, financial investments, and physical processes. It can also be used to make predictions and solve problems in fields such as engineering, physics, and economics.