Final answer:
Polynomials of the form p(t) = a + t^2 are known as quadratic functions, and they represent parabolas that open upward on a graph. The constant term 'a' affects the vertical shift of the parabola.
Step-by-step explanation:
When we talk about polynomials of the form p(t) = a + t2, we are referring to quadratic functions, which are a specific type of second-order polynomial. These functions are defined by an equation where the highest power of the variable is 2. In the function p(t) = a + t2, a represents a constant term and t2 represents the quadratic term. The graph of this function will be a parabola that opens upward, due to the positive coefficient of the t2 term.
The solution of quadratic equations is found using the quadratic formula when the equation is set to zero; however, in the form given here, the equation is not set to zero and instead represents the general form of the polynomial function. If you were to graph this function using an equation grapher, you would see how the constant term a shifts the parabola up or down along the vertical axis.