Quadratic equations Questions and Answers

8 Graph the following system of inequalities to determine the solution Please heavily shade the area that provides your solutions 3 y x 2 x 2 y 6 9 y x 10 H 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 N 4 6 8

If 320 feet of fence are used to enclose a rectangular pen the resulting area of the pen is A x 160 x where x is the width of the pen Is A a quadratic function What is the maximum area of the pen Is A a quadratic function O No Yes

Consider the dynamical system X k 1 f X k where f x where X X X X3 x x 2x1x2x3 2x1x2x3 x1 x2 x3 Find all its fixed points and analyze their stability

Solve the following system of differential equations w y z 1 w y z 0 w y z 0 w 0 0 w 0 1 y 0 0y 0 0 2 0 1 2 0 1

Do Based on the graphs of f x and g z below answer the following questions If a question has more than one answer in your answer as a list of values separated by commas Thus for example if you think f z g when z when z 29 you would enter 20 25 29 or any other order of these three numbers separated by commas 25 and 20 when 4 9 2 9 2 2 d For what value s of zislare f a g 4 0 52 61 69 8 0 a Firid 6 1 b Fill in the blanks in each of the two points below to correctly complete the coordinates of two points on the graph of ofa 1 29 c For what value s of zisare f x 2 97

Write the expression as a single logarithm 3 log 4 log 9 3 log 4 log 9 Simplify your answer

Solve the inequality using a graph Round your answer to four decimal places 7 3 X 8 X Check

The graph of the function B x is shown below Determine the following values for the function B x 0 B x 1 B x 2 Comp

Expand the following logarithm r 9 log 7 1 s4 3 Choose the correct answer below 1 1 1 OA 2log 7r 2log 79 4 log 7s 3 log 7t Wincente OD BURJALLI 1 O B log 7 r log7 9 4 log7s log 7t 3 1 1 OC log 9 4 log 7s 3 log 7t 1 log 7 r 9 4 log 7s log 7t 1 3 1984

Expand the logarithm Simplify if possible log 8xy Choose the correct answer below O A O B O c O D log 8x log gy log 8x log 8 y log 8x log gy log 8X log 8Y

The graph of F x shown below has the same shape as the graph of G x x but it is shifted up 2 units What is its equation F x 5 OA F x x 2 B F x x2 2 C F x x 2 D F x x 2 5

5 10 pts Use graph paper to find the image of each figure under the given rotation a Rotate ABAT around the point A by a turn angle of 180 B A

3 Solve the following systems inequalities by graphing their solution set 25 x 3y 12 x 2y 25 x y 8 x20 y20 a b

Find the best way to mathematically write the phrase n increased by the product of three and c decreased by 15 Now let n 9 and c 4 and evaluate 1 O 5 1 14 56

Russell and Andy are taking the same math test One question asks them to sketch a graph of f x given the following information the function has degree 4 the leading coefficient is negative the function has zeros as x 4 4 and 6 multiplicity 2 Below are the graphs the two students drew Whose graph is correct Explain all of the reasons how you know Russell s Graph Andy s Graph

Please answer all questions on this sheet Complete the following table for each scenario using the word bank below different negative reciprocal same When solving a system of linear equations between two lines the Slopes are a No solution b One solution any value y intercepts are siis

24 Complete the indirect proof Given 21 m22 and DG is not congruent to FG Prove DE is not congruent to FE Assume that EG EG AEDG AEFG D E Assume the conclusion is false This contradicts the given information so the assumption must be F

The following graph is a translation of the graph of one of the basic functions defined by y x y x y x ory x Find the equation that defines the function Then determine the largest open interval of the domain over which the function is a increasing and b decreasing 10042 CHIED The equation of the function is Type an equation a Find the largest open interval of the domain over which the function is increasing A The open interval is Type your answer in interval notation 8 There is no open interval of the domain over which the function is increasing b Find the largest open interval of the domain over which the function is decreasing OA The open interval is Type your answer in interval notation OB There is no open interval of the domain over which the function is decreasing

10 8 6 4 2 2 12 10 8 6 4 2 2 4 10 12 14 Find an equation for the graph above 2 4 6 8 10 o

Here are the shopping times in minutes for a sample of 23 shoppers at a particular clothing store 26 23 44 41 38 35 31 28 25 22 43 40 37 34 31 27 24 36 36 33 33 33 30 Send data to calculator Draw the histogram for these data using an initial class boundary of 21 5 an ending class boundary of 46 5 and 5 classes of equal width Note that you can add or remove classes from the figure Label each class with its endpoints Frequency 0 00 00 0 X

9 10 marks Consider the graph of the function on the right a Find the domain and the range of f b List the intercepts c Find 0 and 6 d For what value of x does x 3 30 e Solve f x 0 5 a 6 3 Use your knowledge of transformations for the following f Graph y f x 2 Graph f x 0 3 5 2 3 2 4 4 3 9 at 6 0 10 0 11 1 8 2 11 x

State 1 Nevada 2 Arizona 3 Utah 4 Idaho 5 Georgia Growth rate 2 93 2 81 2 55 2 43 2 17 SOURCE U S Census Bureau Population in thousands 2 565 6 339 2 645 1 499 9 545 State 46 New York 47 Vermont 48 Ohio 49 Michigan 50 Rhode Island Growth rate 0 08 0 08 0 03 0 30 0 36 Population in thousands 19 298 621 11 467 10 072 1 058 The table lists the states with the highest and with the lowest population growth rates Use the model P P 1 r where P is the population from the table as of July 2007 x is number of years after July 2007 P is the projected population and r is the growth rate In how many years will the population of Michigan decrease by 1 million Round to the nearest whole number The population will decrease by 1 million years after July 2007 Hint Don t forget to convert the rate to decimal form

Suppose that from the beginning of 2007 to the beginning of 2015 a country consumed gasoline at a rate of about q t 1 6t 141 billion gallons per year 0 sts 8 t is the number of years since 2007 During the same period the price of gasoline was approximately p t 3 5 2 38e 0 5 dollars per gallon Use an integral to estimate to the nearest 10 billion dollars the total spent on gasoline during the given period HINT Rate of spending billion

8 points The following is a student solution to the inequality 1 2 3 4 5 6 7 8 5 18 550 650 L 2 9 6 2 x 4 S 6 3 x 4 9 2x 2 29 S 2r 2 18 VI VI 36 3x 4 18 5 2x 2 3x 4 5 2x 2 3x 4 7 2x 3x 4 5x 11 11 VI 49 2 5 There are two mathematical errors in this work Identify at what step each mathematical errec occurred and explain why it horiatically incorrect

Kim performed a transformation on rectangle ABCD to create rectangle A B C D as shown in the figure below B C D 2 D B P 4 3 A 1 2 3 What transformation did Kim perform to create rectangle A B C D

Which of the following is the characteristic polynomial of 05 5 6 6 1 7 0 1 3 01 0000 a b c d

Write the equation in logarithmic form 12 1 20 27 Select one O a O b log3 O e 1 27 1 log3 3 O c none of the answers are in correct form O d 11 1091 3 3 1 3 1 log1 3 27 1 27 1 27 3

The adult population of a city is 1 150 000 A consultant to a law firm uses the function below to estimate the numbe of people P t who have heard about major crime t days after the crime was first reported About how many days do it take for 60 of the population to have been exposed to news of the crime Round to the nearest whole number P t 1 150 000 1 e 0 03 It takes days Answer

Write the equation in exponential form log a b C 16 a b a b 6 c 16 a b C Select one O A a OB b O C C OD d c c16 a b C d a b 16

Use a graphing utility to graph the polynomial function defined by the left side of the equation below Use end behavior to obtain a complete graph Then use the graph s x intercepts to find the solution to the equation 2x 5x 14x 8 0 Choose the correct graph below O A G OB All graphs are 10 10 1 by 30 30 6 The solution set for the equation is Use a comma to separate answers as needed Q G O C G N Q

6 3 The arc of a soccer ball kicked from the ground follows a path that is shaped like a parabola The arch created by the ball is 64 feet wide and 16 feet high 15 12 9 6 3 10 20 30 40 50 Use the description of the ball s journey above to label the three points on the graph modeling the path of the ball through the air Find a quadratic function B that models the soccer ball s height 60

10 Calculate the inverse and reciprocal differences for the support points Xi 0 1 1 2 2 fi 1 3 3 5 3 3 5 and use them to determine the rational espression p2 2 r whose numerator and denominator are quadratic polynomials and for which 2 2 xi fi first in continued fraction form and then as the ratio of polynomials

Divide using synthetic division 4x 3x 18 x 4 4x 3x 18 x 4 X 4 Simplify your answers Do not factor

Use the figure to solve the inequality g x 0 16 12 8 16 12 2 0 Aga 4 8 12 12 16 x 8 00 xl 2 x 2 2 2 xlx 2 or x 2 2 or 2 xlx 2 or x 2 2 or 2 xl 2 x 2 2 2

Find the domain of f Enter your answer using interval notation x 9 f x x 7

For the rectangular parking area of the shopping center shown which one of the following equations says that the area is 50 000 yd A x 3x 200 50 000 B x 3x 200 50 000 CHE Equation says that the area is 50 000 yd Type A B C or D E11 C O C 2x 2 3x 200 50 000 D x 3x 200 50 000 OB 422 1801 CIR 3x 200 Ba TEMAN 01 CAPE COD

tion 5 10 10 8 6 4 2 Slope m 8 6 4 2 2 4 6 8 10 2 Find the slope of the line 4 6 Enter your answer as an integer or as a reduced fraction in the form A B

2 Dexter was asked to mix the punch for his sister s birthday party He has to figure out how much water and pure concentrate to add How many liters of pure concentrate should be added to 10 liters of 20 concentrate to make a 50 concentrate punch answer liters

2 Given the following function x 8x 16 a Factor completely b What are the x intercepts c What is f 1 d What is the domain and range e Find the inverse of the function f What is the domain and range of the inverse g What is the relationship between the domains and ran of a function and its inverse h Will the domain and range of all functions and their inverses follow this same pattern

1 Change the equation 3x 4y 5 0 into an equivalent equation written in the slope intercept form 3 10 00 5 O y x y x 5 12 O y x 25 0 O y x 520 3

Consider the following functions Step 3 of 4 Find fg 1 Answer How to enter your answer opens in new window f 3 2 1 5 3 4 2 4 and g 1 2 3 4 5 2 5 1

4 A candy store is purchasing two types of candy mix one with milk chocolate and one with white chocolate There are two types of mixes one with nuts and one without nuts The one with nuts is 50 00 per bag and has 5 lbs of milk chocolate and 3 lbs of white chocolate The one without nuts is 6 00 per bag and has 1 lb of milk chocolate and 2 lbs of white chocolate They need 120 pounds of milk chocolate and 450 pounds of white chocolate They have to pay 3000 for the candy a Write a system of inequalities Let a represent the number of bags with nuts and y represents the number of bags without nuts b Graph each equation and shade the solution area Describe the graph you have created c Use linear programming to find the maximum amounts of milk chocolate and white chocolate that can be purchased d How many bags with nuts would be best to order and

3 Barry s Burger Barn opened 25 franchises in its first year of operation The second year they opened 30 additional franchises They opened 35 more in the third year and 40 more in the fourth year If this pattern holds for all future years perform the following a Determine how many new franchises Barry s will open each year in year 5 year 14 and year 26 Explain how you did this b Determine how many total franchises Barry s will have in operation in year 10 year 22 and in year 50 Explain how you did this c How did you determine your answers Relate the relevant information in the story problem above to your

8 Solve the following equation using the quadratic formula 2x 1 749x 0 728 0 O 4 503 O 3 139 and 6 849 O 0 353 and 4 888 O 1 067 and 0 682 O 0 032 This quadratic has no solution

What is the cross section of a right cylinder that is perpendicular to the base O Circle O Rectangle Square O Triangle

10 Rewrite the following using only positive exponents 2 3 3x y5 O O O 3 2y5 3x 25 3y5 2 25 2 3x 11 Evaluate without a calculator State your answer in number form 3 4 answer

P x x 2x 6x 45 d x x 5 P x x 5

What is proof that the period for sine and cosine is 2 b Show your work

4 Write the linear equation in standard form 14y 37 x 15 Identify the function given y 18x O constant function O absolute value function O step function O direct variation function

19 Multiply out the following expression 4a a 6 a 6 O 4a 144a O4a 48 144a O4a 36 O 4a 12a