The vertex form of a parabola is y = a(x – h)² + k, where (h, k) denotes the vertex. Plug in the point (3, -3) into the vertex form to get y = a(x – 3)2 – 3. The correct answer is (A).

You can plug in to make sense of this equation. Say that x = $100. The amount of the keg would then be $107 + $17. The $17 must be the untaxed deposit since it is a flat fee rather than percentage based. Therefore, the tax is $7, which is 7% of the original $100 base price. The answer is (C).

Whenever there are variables in the question, plug in. Be sure to plug in a number that is divisible by 3. Let d = 300. ​\( \frac{1}{3} \)​ of the original amount of $300 is $100, and that is deducted by the company, leaving Syed with $200. Now, subtract the wire transfer fee to get $200 – $30 = $170, which is the target number. Plug in 300 for d in the answers to see which answer is equal to the target number of 170. In (A), ​\( \frac{1}{3} \)​(300) – 30 = 70. This is not the target number, so eliminate (A). Likewise in (B), ​\( \frac{1}{3} \)​(300 – 30) = 90, and in (C), ​\( \frac{2}{3} \)​(300 – 30) = 180. Neither of these is the target number, so eliminate (B) and (C). In (D), ​\( \frac{2}{3} \)​(300) – 30 = 170, which is the target number. The correct answer is (D).

All of the answers are written in the slope-intercept form y = mx + b, where b is the y-intercept and x and y are points on the line. Eliminate (D) because the y-intercept in that equation is 2. For the remaining answer choices, plug in the x- and y-values to determine which equationworks. If x = 1 and y = 6, (A) becomes 6 = ​\( \frac{1}{2} \)​(1) + 4. Solve both sides of the equation to get 6 = 4. Eliminate (A). Choice (B) becomes 6 = 1 + 4​\( \frac{1}{2} \)​, so eliminate (B). Choice (C) becomes 6 = 2(1) + 4, or 6 = 6. Therefore, the correct answer is (C).

Whenever there are variables in the question and the answer choices, think Plugging In. If 2 purchases were made, then p = 2, and the number of bonus points can be calculated as 4(2) + 7 = 8 + 7 = 15. If the number of purchases were then increased by 3, the new p equals 5 and the number of bonus points can be calculated as 4(5) + 7 = 27. The bonus points increased by 27 – 15 = 12. Therefore, the correct answer is (C).