The equation 2x2 − 12x + 1 = 0 is being rewritten in vertex form. Fill in the missing step. Given 2x2 − 12x + 1 = 0 Step 1 2(x2 − 6x ___) + 1 ___ = 0 Step 2 2(x2 − 6x + 9) + 1 − 18 = 0 Step 3 ✔ 2(x − 3)2 + 17 = 0 2(x − 3)2 − 17 = 0 2(x + 3)2 − 17 = 0 2(x − 6)2 − 17 = 0 Question 3(Multiple Choice Worth 1 points) (08.02 MC) The function f(x) = −x2 + 16x − 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles sold. Determine the vertex, and explain what it means in the context of the problem. (6, 10); The vertex represents the maximum profit. (6, 10); The vertex represents the minimum profit. (8, 4); The vertex represents the minimum profit. (8, 4); The vertex represents the maximum profit. Question 4(Multiple Choice Worth 1 points) (08.02 MC) Solve for x: −2(x − 2)2 + 5 = 0 Round your answer to the nearest hundredth. x = 3.58, 0.42 x = 4.52, −0.52 x = −3.58, −0.42 x = −4.52, 0.52 Question 5(Multiple Choice Worth 1 points) (08.02 MC) A yoga studio sells monthly memberships. The function f(x) = −x2 + 50x − 264 models the profit in dollars, where x is the number of memberships sold. Determine the zeros, and explain what these values mean in the context of the problem. x = 6, x = 44; The zeros represent the number of monthly memberships that produces a maximum profit. x = 6, x = 44; The zeros represent the number of monthly memberships where no profit is made. x = 25, x = 361; The zeros represent the number of monthly memberships where no profit is made. x = 25, x = 361; The zeros represent the number of monthly memberships that produces a maximum profit. Question 6(Multiple Choice Worth 1 points) (08.02 MC) The owner of a video game store creates the expression −2x2 + 28x + 20 to represent the store's weekly profit in dollars, where x represents the price of a new video game. Choose the equivalent expression that reveals the video game price that produces the highest weekly profit, and use it to determine that price. −2(x − 7)2 + 118; x = $7 −2(x − 7)2 + 118; x = $118 −2(x2 − 14x) + 20; x = $14 −2(x2 − 14x − 10); x = $10 Question 7(Multiple Choice Worth 1 points) (08.02 MC) The height of a hockey puck that is hit toward a goal is modeled by the function f(x) = −x2 + 8x − 10, where x is the distance from the point of impact. Complete the square to determine the maximum height of the path of the puck. −(x − 4)2 + 26; The maximum height of the puck is 26 feet. −(x − 4)2 + 26; The maximum height of the puck is 4 feet. −(x − 4)2 + 6; The maximum height of the puck is 4 feet. −(x − 4)2 + 6; The maximum height of the puck is 6 feet. Question 8(Multiple Choice Worth 1 points) (08.02 LC) Complete the square to transform the expression x2 + 6x + 5 into the form a(x − h)2 + k. (x + 6)2 + 4 (x + 6)2 − 4 (x + 3)2 − 4 (x + 3)2 + 4 Question 9(Multiple Choice Worth 1 points) (08.02 MC) Which of the following reveals the minimum value for the equation 2x2 − 4x − 2 = 0? 2(x − 1)2 = 4 2(x − 1)2 = −4 2(x − 2)2 = 4 2(x − 2)2 = −4 Question 10(Multiple Choice Worth 1 points) (08.02 MC) The expression 8x2 − 64x + 720 is used to approximate a small town's population in thousands from 1998 to 2018, where x represents the number of years since 1998. Choose the equivalent expression that is most useful for finding the year where the population was at a minimum. 8(x − 4)2 + 592 8(x − 4)2 − 592 8(x2 − 8x + 90) 8(x2 − 8x) + 90