Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8. h = -16t^2+v_0t+s_0, for t

Key Concepts

Quadratic Equations

A quadratic equation is a polynomial equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0. In the context of the given equation, h = -16t^2 + v_0t + s_0, it represents a parabolic relationship between the variables, which can be solved for t using methods such as factoring, completing the square, or the quadratic formula.

Isolating Variables

Isolating a variable involves rearranging an equation to solve for that specific variable. In this case, we need to manipulate the equation h = -16t^2 + v_0t + s_0 to express t in terms of h, v_0, and s_0. This process often requires moving terms to one side of the equation and applying algebraic operations to simplify.

Discriminant

The discriminant is a component of the quadratic formula, given by b^2 - 4ac, which determines the nature of the roots of a quadratic equation. In solving for t in the equation h = -16t^2 + v_0t + s_0, the discriminant helps identify whether the solutions for t are real and distinct, real and repeated, or complex, influencing how we interpret the results.