Final answer:
The question involves solving a quadratic equation using the quadratic formula. The constants given are used to find the solutions of the equation. The domain and range describe all possible values of the variable and the function, respectively.
Step-by-step explanation:
The student is asking about the characteristics of a quadratic equation. Quadratic equations are algebraic expressions of the second degree, which means they include a variable that is raised to the power of two. The standard form of a quadratic equation is at² + bt + c = 0, where a, b, and c are constants, and t is the variable.
To find the solutions to a quadratic equation, you can use the quadratic formula: t = [-b ± √(b² - 4ac)] / (2a). Given the values a = 4.90, b = -14.3, and c = -20.0, you can substitute these into the quadratic formula to find the values of t that satisfy the equation. Remember, the domain of a quadratic function is always (-∞, ∞), meaning that the variable t can take on any real value. Meanwhile, the range describes the possible values of the quadratic function, which in this case is (-∞, -2] since (-2) is the y-value of the vertex, and the parabola opens upwards.