January 2016 Algebra 1 (Common Core) Regents, part 11. In the role f(x) = (x - 2)2 + 4, the minimum worth occurs as soon as x is(2) 2. The crest is at the point (h, k) taken native the basic form, f(x) = (x - h)2 + k.2. The graph listed below was produced by one employee at a gas station. (image omitted)Which statement have the right to be justification by utilizing the graph?(2) because that every gallon that gas purchased, $3.75 to be paid. (1) and also (3) deserve to be eliminated by checking the graph. Neither (10, 35) nor ((2, 5) are points on the line. Girlfriend can"t view (1, 3.75) yet if you multiply by 4, girlfriend will view (4, 15) on the graph. An option (4) is just ridiculous -- the graph has nothing to do with mile driven.3. because that a freshly released movie, the function y = 119.67(0.61)x models the revenue earned, y, in millions of dollars each week, x, for several weeks after ~ its release.Based ~ above the equation, exactly how much more money, in numerous dollars, to be earened in revenue because that week 3 than for week 5?(3) 17.06. Substituting 3 because that x in the function gives us about 27.16 million, and also substitution 5 offers us 10.11, through a distinction of 17.05. The distinction with the answer is a minor round off error.4. Given the complying with expressions: I. -(5/8) + (3/5); II. (1/2) + sqrt(2); III. (sqrt(5))*(sqrt(5)); IV. 3*(sqrt(49))Which expression(s) result in an irrational number?(1) II only. The an initial is the sum of 2 rationals, which is rational. The 2nd is the sum of a rational and an irrational, i m sorry is irrational. The third squares the square root of 5, i beg your pardon is 5, a reasonable number. The critical is 3 times the square source of 49, which equates to 3 * 7 i m sorry is 21, a reasonable number.5. i beg your pardon inequality is represented by the graph below?(2) y > 2x - 3. The y-intercept is -3. The slope is 2. The graph is shaded over the line. (The line is likewise solid, but that doesn"t matter for the options given.)6. Michael lend money indigenous his uncle, who is charging him simple interest utilizing the formula i = Prt. To figure out what the interest rate, r, is, Michael rearranges the formula to find r. His brand-new formula is r equals(3) I/Pt. Division both sides of the equation by P and also t to isolate r.7. i m sorry equation is equivalent to y - 34 = x(x - 12)?(4) y = (x - 6)2 + 2.Distribute the x and you get: y - 34 = x2 - 12x.Add 34 to both sides: y = x2 - 12x + 34.There are no integer components of 34 that have a sum of -12. (Eliminate choices 1 and 2.) This way completing the square, OR working backward native the other choices. Squaring (-6) offers us +36. To make 36 right into 34, we have to subtract 2. Selection (4).8. The equation A = 1300(1.02)7 is being supplied to calculation the lot of money in a to save account. What does 1.02 stand for in this equation?(4) 2% growth. It"s better than 1, so it is growth. (And if it is a savings account, it far better be growth, or why have the account?) The decimal .02 is 2% as a percentage.9. The zeros the the role f(x) = 2x2 - 4x - 6 are(1) 3 and -1. Plugin the numbers and also see what gives you 0. This is probably faster than factoring.2x2 - 4x - 6 = 0x2 - 2x - 3 = 0(x - 3)(x + 1) = 9x = 3 or x = -110. When (2x - 3)2 is subtracted native 5x2, the an outcome is
(3) x2 + 12x - 9.5x2 - (4x2 - 12x + 9) = 5x2 - 4x2 + 12x - 9 = x2 + 12x - 9.11. Joe has a rectangular patio that steps 10 feet by 12 feet. He wants to rise the area by 50% and also plans to rise each dimension by same lengths, x. I beg your pardon equation might be offered to identify x?(2) (10 + x)(12 + x) = 180. Area = size * width = (10)(12) = 120. Increasing 120 through 50% method 120 + .5(120) = 180.12. once factored completely, x3 - 13x2 - 30x is (3) x(x + 2)(x - 15)x(x2 - 13x - 30) = x(x - 15)(x + 2)13. The table listed below (image omitted) shows the cost of e-mail a postcard in different years. Throughout which time interval did the price increase at the biggest average rate?(4) 2006-2012. Discover the median rate for each interval. Indigenous 1898-1971, the readjust was 5/73. Indigenous 1971-1985, it to be 8/14. Indigenous 1985-2006, it was 10/21. Indigenous 2006-2012, it to be 11/6. An option (4) is the just one better than 1, so it is clearly the greatest.If girlfriend eliminate choice 1 together obviously an extremely flat, you have the right to sketch out the various other points and see that 2006-2012 is the steepest line.14. When resolving the equation x2 - 8x - 7 = 0 by perfect the sqaure, which equation is a step in the process?(2) (x - 4)2 = 23. Half of 8 is 4, for this reason eliminate selections (3) and (4). (-4)2 = +16. You have to include 16 to both sides AND add 7 come both political parties to obtain the 7 to the various other side the the equation. 16 + 7 = 23.15. A construction agency uses the duty f(p), wherein p is the number of of people working top top a project, to model the quantity of money that spends to finish a project. A reasonable domain for this duty would be (1) positive integers. The variety of people has to be a count number. It can not be negative nor a fraction. World can also be zero, but in the context of the problem, if zero human being are working on a project, the firm won"t make any money. (None that the choices include zero.)16. Which duty is presented in the table below? (image omitted)(4) f(x) = 3x. Substitute 0 into the functions and also only choice (4) works. For the matter, choice (4) is the just one that can create fractions as output once the entry is integers.17. Given the attributes h(x) = 1/2x + 3 and f(x) = |x|, which value of x makes h(x) = f(x)?(1) -2. It is much faster to occupational backward indigenous the answers given. 1/2(-2) + 3 = -1 + 3 = 2 = |-2|18. Which recursively defined function represents the sequence 3, 7, 15, 31 ... ?(3) f(1) = 3, f(n + 1) = 2f(n) + 1. Each term ~ the first is one an ext than twice the vault term. Note: ns don"t know if there space typos in options (1) and also (2) or if it was intended to create f(n) together an exponent. It"s just odd-looking. Together an exponent or not, the answers are incorrect, so the doesn"t matter.19. The range of the role defined together y = 5x is (2) y > 0. A optimistic number to any type of exponent will certainly be positive, never zero or negative.20. The graph the y = f(x) is displayed below. (image omitted)What is the graph of y = f(x + 1) - 2?(1). The graph will move 1 an are to the left and 2 down since h = -1 and also k = -2.21. Which pair that equations might not be supplied to solve the adhering to equations because that x and also y?4x + 2y = 22-2x + 2y = -8(4) 8x + 4y = 44; -8x + 8y = -8. In options (1) - (3), one or both of the equations is multiplied by some constant. In (4), the -8 was not multiplied through 4 however the left next of the equation was.22. The graph representing a duty is presented below. (image omitted)Which function has a minimum the is less than the one displayed in the graph?The graph has a minimum at (3, -7). This eliminates choices (2) (-3, -6) and (4) (8, 2). In choice (1), the axis of symmetry is 3, and also the y-coordinate the the peak is y = (3)2 - 6(3) + 7 = 9 - 18 + 7 = -2In an option (3), the axis of the contrary is 1, and the y-coordinate that the peak is y = (1)2 - 2(1) - 10 = 1 - 2 - 10 = -11.Alternatively, you might have put these right into your graphing calculator and also just it was observed the correct answer.23. Grisham is considering the three situations below.I. For the first 28 days, a sunflower grows at a price of 3.5 cm per day.II. The worth of a car depreciates in ~ a rate of 15% per year after that is purchased.III. The quantity of bacteria in a culture triples every 2 days throughout an experiment.Which the the statements explain a instance with an equal difference over an same interval?(1) I, only. The an initial situation is a direct function, farming the exact same amount every day. (Constant slope.) The other two space exponential functions with the amount an altering from interval come interval, even if the portion remains the same.24. After performing analyses ~ above a set of data, Jackie examined the scatter plot that the residual values for every analysis. I m sorry scatter plot indicates the finest linear fit because that the data? (images omitted)(3). The residual plot need to contain randomly-scattered points above and below the x-axis. It must not have actually a pattern to it.
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Choices (1), (2) and also (4) present curve-like fads to the plot of their residuals. These suggest a bad fit because that the data.End of component I