Quadratic equations Questions and Answers

A hairstylist charges 15 for an adult haircut and 9 for a child haircut She wants to earn at least 360 dollars and cut a maximum of 30 haircuts this week The graphs represent the hairstylist s constraints number of child haircuts VERSOS 45 40 35 30 15 10 5 5 10 15 20 25 30 35 40 45 number of adult haircuts List two points that could represent the numbers of adult and child haircuts that meet the hairstylist s goals

3 For the function defined by 2x 1 xs1 Part I Evaluate 0 A Identify the function that will be used when x 0 1 point B Find the value of this function when x 0 1 point f 0 0 2 0 Part II Graph f x A Graph the first function completely 1 point B On the same graph you used to answer part A graph the second function completely 1 point C Identify the value of x at which the functions change Remove the parts of each line that are not included in domain of the corresponding function 2 points D Place open and closed circles appropriately on the

94 7 2 ya CCTV usilly Tuvivu s To multiply the denominators use the equation A B A B A B 94 7 2 49 2 94 7 2 7 2 7 2 Simplify the denominator O 94 7 2 94 7 2 49 2 47 Is there a common factor in the numerator and denominator Yes No uvu Divide the numerator by the denominator 94 7 2 47 7 2 Multiply

Kavita has been assigned the task of studying the average customer receipt for a branch of a major restaurant chain The average receipt for the chain is 72 00 with a standard deviation of 11 00 The branch she is studying has an average bill of 67 00 for the last 40 receipts She needs to know if this falls below the chain s average She will use a 1 level for significance because she does not want to inadvertently report the restaurants income as below average a Critical z values Upper Tail Values 5 1 65 2 5 1 96 1 2 58 Which choice depicts the result for Kavita s hypothesis test She should reject Ho 72 and accept Ha 72 She should reject Ho 72 and accept Ha H 72 72 O She should accept Ho 72 and reject Ha She should reject Ha 72 but cannot accept Ho 72

81 log 147 log 3 B 3 C 2 logs 8 A 4 D 1

7 Cual de estos n meros es un factor de 18 y 42 O O O O A 4 B 6 C 7 D 9

50 spins She computes and graphs the relative frequencies for each number Which of the following describes the probability distribution Px x 0 6 0 5 0 4 0 3 Relative Frequency of Numbers Spun 0 2 0 1 0 O constant 1 symmetric 2 3 X 5

The graphs on the right show the percentage of jobs in a country s labor force held by men and women from 1970 through 2010 The formula p 2 3 t 33 2 models the percentage of jobs in the labor force p held by women t years after 1970 Answer parts a through c Percentage of Jobs Percentage of Jobs Held by Men and Women 80 66 8 70 60 50 40 30 20 10 0 1970 1980 33 2 Men Women 1990 Year 52 3 47 7 2000 2010 Q Q a Use the appropriate graph to estimate the percentage of jobs in the labor force held by women in 2000 Give your estimation to the nearest percent p 46 Round to the nearest whole number as needed b Use the mathematical model to determine the percentage of jobs in the labor force held by women in 2000 Round to the nearest tenth of a percent p 45 8 Round to the nearest tenth as needed c According to the formula when will 55 of jobs in the labor force be held by women Round to the nearest year 55 of jobs in the labor force will be held by women by

When a draftsman draws three lines that are to intersect at one point the lines may not intersect as intended and subsequently will form an error triangle If this error triangle is long and thin one estimate for the location of the desired point is the midpoint of the shortest side The figure shows one such error triangle a Find an estimate for the desired intersection point b Find the length of the median for the midpoint found in part a a The estimate for the desired intersection point is Ay 2 2 2 1 8 1 6 1 4 1 2 1 6 TEHN 1 7 1 5 2 3 0 1 9 2 4 2 9 1 7 2 8 3 2

xs 1 Choose the correct answer below OA O C 12 10 12 10 8 8 6 6 Write the solution in interval notation 4 4 Type your answer in interval notation 2 2 0 2 0 2 4 4 6 8 6 8 10 10 CHEE 12 12 B D 12 10 12 10 8 8 6 6 4 4 2 2 0 0 2 2 4 4 6 6 8 8 10 10 12 12

Find the domain of the function f x x 5x 3 What is the domain of f OA 0 0 U 0 00 OB 3 U 3 00 O C 00 00 D 3 U 3 0 U 0 00

5 Explain in your own words the process for how to add or subtract radical expressions Then simplify the expression Show all steps Assume all variables represent positive numbers xv10x 3 80x x 245x

x 13 Solve for x x 55 X x

y 1 1 100y3 200y2 100y 10y2y3 10y2e0 1 0 2 100y4 200y3 100y2 10y3y4 10y3e0 2 0 3 100y5 200y4 100y3 10y4y5 10y e0 0 4 100y6 200y5 100y4 10y5Y6 10y e04 0 5 100y7 2006 100y5 10y6y7 10y e0 5 0 6 100y8 200y7 100y6 10y7y8 10y e06 0 7 100y9 200y8 100y7 10y8Y9 10y e0 7 0 8 100y10 200y9 100y8 10y9y10 10y e0 8 0 9 Y10 1 10 put these equations and solve them using matrix

graphing by plotting po For the equation find three ordered pair solutions by completing the table Then use any two of the ordered pairs to graph the equation 1 y 7x Complete the table below y X 0 8 0 Question 2 3 2 13 Part 2 of 4 GCIOS 10 HW Score 44 44 4 of 9 points O Points 0 of 1 0 Q Q

plotting po For the equation find three ordered pair solutions by completing the table Then use any two of the ordered pairs to graph the equation 1 y 4 Complete the table below y x 0 8 8 0 2 H Part 3 of 4 10 Points 0 of 1 10 8 4 Ay 2 17 Q

A 49 ft boom on a crane is attached to the crane platform at point D A cable is attached to the end of the boom at point B and to a 14 ft A frame at point anchored by the counterweight If LBDA is 82 2 find the length of the cable to the nearest tenth of a foot Round intermediate steps to at least four dec places 49 ft D 14 ft

Find the area of this triangle if C 138 a 16 and b 7 B square units Round to the nearest tenth Enter

2 The loudness L of a sound in decibels dB can be calculated using the formula L 10 log I in the intensity of the sound in watts per square metre W m and Io 10 12 W m A teacher is speaking to a class Determine the intensity of the teacher s voice if the sound level is 70 dB 2 marks

What is the magnitude of V 5 9 1 Round to the nearest hundredth Enter

A fire truck is to be added to a certain Municipality Use Huntington Hil apportionment Method Municipality East West North South No of fire truck No of Houses Huntington Hill No 6 8 10 12 464 608 751 893 Which municipality should get the fire truck 5126 5112

17 Suppose f x x 10x 21 and g x At which of these points does the function y f x g x h x 2 x 3 a hole d 3 0 a 2 0 b 7 0 c 2 3

1 point The function f x 3x x is given graphed below Note Click on graph for larger version in new browser window A Starting with the formula for f x find a formula for g x which is graphed below g x Note Click on graph for larger version in new browser window B Starting with the formula for f x find a formula for h x which is graphed below Note Click on graph for larger version in new browser window

What is the direction of w 5 2 W degrees Round to the nearest hundredth Enter

dentity the graph of y 6x Choose the correct graph below OA OB O C

Each line to the right has a negative slope Find the slope of each line Find the slope of L O Type an integer or a simplified fraction 0 LO 8 0 2 24 04

The following function is graphed in a window that results in hidden behavior Experiment with various windows to locate the extreme points on the graph of the function Round values to the nearest hundredth y x 11x 40x 45 10 10 by 1 10 103 Xacl 1 Yscl 1 Determine an appropriate window for the given graph OA 1 3 1 by 3 6 OB 1 6 21 by 1 6 OC 1 8 41 by 1 4 OD 10 4 by 6 11 The local maximum point is Type an ordered pair Round to the nearest hundredth The local minimum point is Type an ordered pair Round to the nearest hundredth

find the slope and intercept of 4 1 2y 2x

Find the equation of the graph given below Note Enter your answer in cosecant form 7 3 7 6 Provide your answer below 5 4 3 2 1O 0 3 2 TT 2 0 2 31 5 TT 2 TT 7 3 3TT 2 2TT 5TT 2 3TT

What is the range of the absolute value function below 2 1 234 K 74 1 Of x 2 4 O f x 2 1 Of x 1 Of x 4 3 4 HH 7 8 Save

What is the vertex of the absolute value function below 2 1 1 1 2 4 ch 7 O 4 1 O 1 4 O 1 4 0 4 1 m Ma 2 3 4 5 mm 6 N 00 8 X

Consider the table showing the given predicted and residual values for a data set X 1 2 3 4 Given 1 6 2 2 4 5 6 1 Predicted 1 2 1 5 4 7 6 7 Residual 0 4 0 7 0 2 0 6 Which point would be on the residual plot of the data O 1 1 6 O 2 1 5 O 3 4 5 O 4 0 6

Which function is a translation of the parent absolute value functio O f x 2x O f x x 61 O f x x O f x 4 x

What is the vertex of the absolute value function below 3 2 O 3 2 2 3 7 8 O 2 3 6 4 3 ONE 7 6 5 4 3 2 1 543211 2 2 y CHE 1 2 3 X

Solve the inequality giving its solution set in both interval and graph form 4x 92 11x What is the solution set Select the correct choice below and if necessary fill in the answer box within your choice A The solution set is Type your answer in interval notation Simplify your answer Use integers or fractions for any numbers in the expression B The solution set is Choose the correct graph O A SOB O C O D 6 6 6 5 5 4 3 3 2 2 1 1 0 0 0 2 2 2 3 3 4 5 5 6 6

The quadratic function fis represented by the equation f x x2 2x 2 The table gives some of the values of the exponential function g x 0 1 3 0 7 X 1 g x 0 5 Which of the following statements is FALSE f 3 g 3 2 3 The functions f x and g x have the same value at x 1 Both functions have a domain of all real numbers The y intercept of f x is greater than the y intercept of g x

The graph to the right shows the region of feasible solutions Find the maximum and minimum values of the objective function objective function 7x 3y GLICE The maximum value of the objective function is at point 2 9 2 0 8 5 187 O a C

me Left 1 12 51 Use a graphing utility to determine how many distinct real solutions the following equation has z 4 3 2 Oo Juelz James McCray Attempt 1 2 I 2 z 3 infinitely many

estion 17 Given the Vertex 2 0 and point on graph 4 12 find the equation of the quadratic function work for this problem on your scratch paper

Consider the plot created from the residuals of a line of best fit for a set of data 0 0 X Does the residual plot show that the line of best fit is appropriate for the data O Yes the points have no pattern O Yes the points are evenly distributed about the x axis O No the points are in a linear pattern O No the points are in a curved pattern

Consider the graph of the line of best fit y 0 5x 1 and the given data points 2 2 X which is the residual value when x 2 0 2 O 1 O 1 02

Suppose that f x 5x 1 and g x 4x 8 a Solve f x 0 b Solve f x 0 d Solve f x g x c Solve f x g x e Graph y f x and y g x and find the point that represents the solution to the equation f x g x

Naomi wants to save 100000 so she makes quarterly payments of 1500 into an account that earns 4 4 a compounded quarterly How long will it take her to reach her goal

The chart to the right shows a country s annual egg production Model the data in the chart with a linear function using the points 0 51 7 and 4 60 4 Let x 0 represent 1994 x 1 represent 1995 and so on and let y represent the egg production in billions Predict egg production in 2000 How does the result compare to the actual data given in the table 69 9 Year Egg production in billions 51 7 52 6 54 4 57 3 60 4 64 69 9 as 1994 1995 1996 1997 1998 1999 2000 The linear model for the data is Type an equation using x as the variable Type your answer in slope intercept form Use integers or decimals for any numbers in the equation Round to the nearest thousandth ded

7 points Determine the vertical horizontal and or oblique asymptotes for the following function SHOW WORK x 1 2 1

This test is worth 23 points To pass you need to earn 14 of them Identify the absolute value inequality that describes the points required t pass Let p represent the actual points earned on the test OP 9 O 23 14 p Op 18 5 4 5 4 O 23 4 5 p 18 5

1 2 3 4 5 6 7 8 9 Which is equivalent to 4xy 3z 2 and what type of special product is it 16x2y 9z the difference of squares O 16x y 92 a perfect square trinomial 16x y2 24xyz 9z2 the difference of squares 16x y 24xyz 92 a perfect square trinomial

Which products result in a perfect square trinomial Select three option O x 9 x 9 xy x xy x 2x 3 3 2x 16 x x 16 4y 25 25 4y

2 A scientist wants to make 6 milliliters of a 30 sulfuric acid solution The solution is to be made from a combination of 20 sulfuric acid solution and a 50 sulfuric acid solution Review Mixture Problems Resources for help a Write a system of equations in two variables to model the relationship b How many milliliters of each solution must be combined to make the 30 solution Show your work 3 Which method of solving a system of equations graphing substitution elimination is best for the system below Explain why your choice is better than the other options You do not need to solve the system 2x 3y 4 2x 5y 6

What are the domain and range of the function f x 4 81 Oxx is a real number yl y 0 x x 4 vy 0 Ox x is a real number yl y 4 xx 4 vy 4