Final answer:
Quadratic word problems fall under the category of c) Algebra, which deals with quadratic functions and algebraic expressions, and are taught at the High School level.
Step-by-step explanation:
The student's question pertains to quadratic word problems and asks which category they fall under among the given options: Calculus, Trigonometry, Algebra, or Geometry. Quadratic word problems are commonly associated with quadratic equations, which are mathematical functions of the form at² + bt + c = 0.
These types of equations are a fundamental part of Algebra, which is a branch of Mathematics that deals with symbols and the rules for manipulating these symbols. The quadratic formula, which is used to find the solutions of quadratic equations, is an essential concept in Algebra.
Figure 1.28 provides examples of different types of relationships represented graphically, including a quadratic relationship. This further supports the understanding that the nature of the problem involves Algebra. Additionally, in the given curriculum for Mathematics Grade 10, we see that Algebraic expressions and Equations are part of the topics covered, signifying the high school level of the question.
In summary, the correct option for the category of quadratic word problems mentioned in the student's question is Algebra, and it is typically taught at the High School grade level.