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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?

a) 1.2b) 2.3c) 16.7 hours

Algebra

Chapter 5

QUADRATIC FUNCTIONS AND COMPLEX NUMBERS

Section 2

The Quadratic Formula

Equations and Inequalities

Quadratic Functions

Complex Numbers

Polynomials

Oregon State University

McMaster University

Harvey Mudd College

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in this question here for part A. We want to find to the nearest 10th B average G p A. Of a student who does know studying. So that's when h is you go to zero. So g of zero is equal to zero point 006 times zero squared plus 0.2 come zero plus 1.2, which is equal to 1.2 carpi. Here we want to find gpm, assume who studies 12 hours. So that's G 0 12 So instead of plugging and zero for each, we plug in 12. So 0.6 times 12 squared pluses. Europeans here, too. Times 12 plus 1.2, which is equal to approximately 2.3. Now, what part C Here we want to find how many hours of studying a required to achieve 3.2. So that means that 3.2 his equal to 0.6 each squared classes your 0.2 h plus 1.2 subtracting 3.2 from both sides of the equation. You got 0.6 h squared plus 0.2 h minus two is you go to the room. Then he used the quadratic formula to solve for when h is equal to zero or what makes a secretion true. So we have a is equal to 0.6 b is equal to 0.2 and C is equal to negative two. And what you'll get is that like your two solutions are 16 points at 667 or negative 20 but obviously are which cannot be negative. 20 because you cannot study negative number of hours, so your solution would be 16.667

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