Based on data from a local college, a statistician...

Based on data from a local college, a statistician determined that the average student's grade point average $(\mathrm{GPA})$ at this college is a function of the number of hours, $h,$ he or she studies each weck. The grade point average can be estimated by the function $\mathrm{G}(h)=0.006 h^{2}+0.02 h+1.2$ for $0 \leq h \leq 20$ . a. To the nearest tenth, what is the average GPA of a student who does no studying? b. To the nearest tenth, what is the average GPA of a student who studies 12 hours per week? c. To the nearest tenth, how many hours of studying are required for the average student to achieve a 3.2 GPA?

Based on data from a local college, a statistician determined that the average student's grade point average $(\mathrm{GPA})$ at this college is a function of the number of hours, $h,$ he or she studies each weck. The grade point average can be estimated by the function $\mathrm{G}(h)=0.006 h^{2}+0.02 h+1.2$ for $0 \leq h \leq 20$ .
a. To the nearest tenth, what is the average GPA of a student who does no studying?
b. To the nearest tenth, what is the average GPA of a student who studies 12 hours per week?
c. To the nearest tenth, how many hours of studying are required for the average student to achieve a 3.2 GPA?

Key Concepts

Solving Quadratic Equations

Solving quadratic equations involves finding the values of the variable that satisfy the equation when the function equals a specific value. This typically requires techniques such as the quadratic formula, factoring, or completing the square, and is essential when determining the input needed to reach a given output.

Quadratic Functions

Quadratic functions are polynomial functions of degree two, typically expressed in the form ax² + bx + c. They often model scenarios with non-linear interactions and can have parabolic shapes with potential maximum or minimum points.

Domain Consideration

Domain consideration involves recognizing the set of acceptable inputs for a function based on the problem context. In real-world applications, such as study hours per week, the domain restricts the function to realistic and meaningful values to ensure valid interpretations.

Function Modeling

Function modeling is the process of representing a real-world situation using a mathematical function. In this context, the relationship between study hours and GPA is expressed as a mathematical function, allowing one to predict or analyze performance based on study time.

Function Evaluation

Function evaluation involves substituting a specific input into a function to calculate the corresponding output. For example, determining a student's GPA by inputting a given number of study hours into the function.

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