When the quadratic is set to 0 the parabola crosses the x-axis at (-20, 0) and (20, 0). Because parabolas are symmetrical, the vertex of the parabola is at (0, 40). Plug this point into the equation to get 40 = a(0 – 20)(0 + 20). Simplify the right side of the equation to get 40 = a(-20)(20) or 40 = -400a. Solve for a to get a = ​\( -\frac{40}{400} \)​ = ​\( -\frac{1}{10} \)​. Therefore, the correct answer is (C).

Whenever the question asks for a specific value and the answer choices are numbers, think Plugging In the Answers. In (A), a = -0.75. Plug -0.75 in for a in the equation to get 16(-0.75)² + 4(-0.75) – 6 = 0. Solve the left side of the equation to get 16(0.5625) + (-3) – 6 = 0, or 9 – 3 – 6 = 0. Since, this statement is true, the correct answer is (A).

So far the zoo has sold 4 × 48 = 192 tickets. To make a profit, the zoo will need to sell at least 350 – 192 = 158 additional tickets. So, z needs to be at least 158. Calculate z in each of the answers to see which gives you a value of z ≥ 158. In (A), z ≤ 350 – 4(48), so z ≤ 158. Eliminate (A). Choice (B) gives you z ≥ 158. Keep (B). Choice (C) gives you z ≥ -158. Eliminate (C). Choice (D) gives you z ≤ -158. Eliminate (D). Choice (B) is the correct answer.

Line 1 shows exponential growth, because the line curves upward. Because birth rate and death rate are per 1,000 people, a birth rate higher than a death rate will result in exponential growth (because births-deaths will increase as the population increases). Immigration and emigration numbers are per year and therefore have a linear effect on the graph (as the absolute change in the population due to immigration-emigration is constant). South Zealand has more births per 1,000 than deaths per 1,000, so (D) accurately reflects line 1.

You can start with Process of Elimination. Since the number of people in the theater decreases over time, you can eliminate (D). Choices (A) and (B) are exponential functions, whereas (C) is linear. The number of people that leave the theater every 15 minutes is not constant, since it is proportional to the number of people currently in the theater; therefore, this function is not linear, and you can eliminate (C). Choice (A) must be correct since the function decreases quickly and then the number leaving every successive 15 minutes is less than the time before (10% of 250 is more than 10% of 225).