# Quadratic equations Questions and Answers

Algebra

Quadratic equationsWhat is the y intercept of the line graphed below 44 744134134 19 A 2 3 4 5 6 7 8 9 Select one O 0 O 2 02 O 1

Algebra

Quadratic equationsGiven the points graphed in the following figure use quadratic regression to find the quadratic function of best fit Round the coefficients to three decimal places if necessary 10 5 101 S Correct 10 Enable Zoom Pan X 4 Keypad Keyboard Shortcuts

Algebra

Quadratic equations6 The Fast Computer store sold 900 computer chips last summer at 15 each Since sales were good last the company decides to increase price by 5 but a survey indicates that for every increase in price the sales of this chip will decrease by 100 a What price will maximize revenue from the sale of the computer chip b What price would result in a revenue of 16 875 Homework p 3 s 5 6 12a b 14

Algebra

Quadratic equations3 The environmental club sells T shirts as a fundraiser They sell 1200 shirts a year at 20 each They ar planning to increase the price A survey indicates that for every 2 increase in price there will be a d sales a year What should the selling price be in order to maximize the revenue

Algebra

Quadratic equationsSA theatre company has 300 season tickets subscribers The board of directors has decided to raise the price of a in pron ticket from the current price of 400 A survey of the subscribers has determined that for every 20 increase in price 10 subscribers would not renew their season tickets What price would maximize the revenue from their season

Algebra

Quadratic equationsEnter the prime factorization of 198 Use exponents for repeated factors Be sure to use the between different fac factorization for 12 can be entered as 2 2 3 or 3 2 2

Algebra

Quadratic equationsAlgebra Prep 2012 Ke Safar Lie Slope of a Line Find the slope of each line 1 A 2 2 zoom in 1 Leave slope as fraction or fraction if it will not simplit INTEGER

Algebra

Quadratic equationsQ1 A farmer is planning on installing a 30 kW solar PV system equipped with 10kWh electricity storage batteries The cost of installation of the panels with inverter is assumed 1 W and the batteries costs 750 kWh Given various efficiencies let us assume that the system with batteries provides a constant 5 kW in average year around a crude assumption but OK for our purpose The batteries need replacement every 5 years and the system has a salvage value of 5 000 at the end of its life 25 years With this system installed the farmer saves the hydro cost that can be assumed 0 18 kWh Assuming a MARR of 8 calculate the NPV of this investment using two approaches a a simple payback approach b discounted cash flow analysis 35

Algebra

Quadratic equationsFactor the polynomial f x Then solve the equation f x 0 f x x 6x 3x 10 www The factored form is f x x 1 x 5 x 2 The solution s to f x 0 is are x Use commas to separate answers as needed If a solution occurs more than once type the solution only

Algebra

Quadratic equationsA polynomial P x and a divisor d x are given Use long division to find the quotient Q x and the remainder R x Express P x in the form P x d x Q x R x P x x 343 d x x 7 x 343 x 7 7 K

Algebra

Quadratic equationsA polynomial P x and a divisor d x are given Use long division to find the quotient Q x and the remainder R x Express P x in the form P x d x Q x R x 3 P x x 512 d x x 8 x 512 x 8 0

Algebra

Quadratic equationsThe graph of a polynomial function is given to the right On the basis of the graph answer the following questions a Find as many factors of the polynomial as possible b Construct a polynomial function with the zeros shown in the graph c Is it possible to find any other polynomial functions with the given zeros d Is it possible to find any other polynomial functions with the given zeros and the same graph a The factor s is are Simplify your answer Use a comma to separate answers as needed 4 400

Algebra

Quadratic equationslogs 4x 2 Solve the following basic exponential equation by rewriting each as logarithmic equation and approximating the value of x a log x 7 b log 4x 1 4 c In x 3 5 3 Solve the following exponential equation by rewriting each as logarithmic equation and approximating the value of x log 3x 2 5 4 a b log 9x log 4x 6 c 3 In 2x 1 2 22 d In 12x 2 In 2 8

Algebra

Quadratic equationsSelect each interval where the function below is decreasing Choose all that apply A B C D 6 x 4 4 x 2 2 x 2 2 x 6

Algebra

Quadratic equationsGraph the solution set of the system of linea x y 9 3x y 1 yeo Use the graphing tool to graph the system Click to enlarge

Algebra

Quadratic equationsSolve the system by graphing 7x 5y 0 8x 5y 5 Use the graphing tool to graph the syster A Click to

Algebra

Quadratic equationsGiven f x 25x 10x 1 answer the following a Graph the function b Determine the domain and range of the function c Determine where the function is increasing and where it is decreasing to separate answers as needed The range is 0 Type your answer in interval notation Use integers or fractions for any numbers in the expression Use a c to separate answers as needed c Determine where the function is increasing and where it is decreasing Select the correct choice below ar if necessary fill in the answer box within your choice OA The function is increasing on the interval s Type your answer in interval notation Use integers or fractions for any numbers in the expression comma to separate answers as needed OB The function is never increasing

Algebra

Quadratic equationsLet f x x and f g x f g x fg x g x x 9 help formulas help formulas help formulas help formulas The domain of f g x is help intervals The domain of f g x is The domain of fg x is help intervals The domain of is help intervals help intervals

Algebra

Quadratic equationsy f x Use the graphs of y f x and y g x above to the find the function value a g 0 help numbers b g g 3 help numbers Ex Evaluate Composite Functions y g x

Algebra

Quadratic equationsa Find two planes in R3 which intersect in the line given by x 2 3t y 1 2t z t Give the equations of the planes and be sure to provide justification that your example has the properties required b Find two different planes which have the same intersection as a and explain why this is possible both geometrically and algebraically

Algebra

Quadratic equationsMarcus has accepted a job selling cell phones He will be paid 1500 plus 15 of his sales each month He needs to earn at least 2430 to pay his bills For what amount of sales will Marcus be able to pay his bills

Algebra

Quadratic equationsA o structure A is called ultrahomogeneous if any o isomorphism between two finitely generated substructures extends to a o automorphism of the whole structure A i e if B C are finitely generated substructures of A and h B C is a o isomorphism then there is a automorphism h of A with h 2 h a Show that Q is ultrahomogeneous The same argument should prove that IR is also ultrahomogeneous b Let Ogph E be the signature for graphs and let G be a graph i e a Ogph structure that is the undirected bi infinite path namely G Z EG where EG x y Z x y 1 Is G ultrahomogeneous Prove your answer

Algebra

Quadratic equationsFind the equation of the line that contains the given point and with the given slope Write the equation in slope intercept form if possible and graph the line 8 2 slope w your IVU Simplify your answer Use integers or fractions for any numbers in the equation A The equation of the line in slope intercept form is y 1 4 X OB The equation of the line cannot be written in slope intercept form The equation of the line is Use the graphing tool to graph the line Click to CHE 10 B 6 4 2 10 8 go 6 4 2 2 4 6 8 40

Algebra

Quadratic equationsAt midnight the temperature was 8 F At noon the temperature was 23 F Which expression represents the increase in temperature A 8 23 B 1 8 23 C 8 23 D 1 8 23 B

Algebra

Quadratic equationsComplete parts a d for the functions f x x 5x and g x x 3x 4 b Solve f x g x The solution set is 2 1 Use a comma to separate answers as needed c Use the result of part b to label the points of intersection of the graphs off and g The points of intersection are 2 6 1 6 Type an ordered pair Use a comma to separate answers as needed d Shade the region between the two curves for which f x g x that is the region below f and above g Choose the correct graph below O A O B O C O D A Q Q G

Algebra

Quadratic equationsM1 Review September 22 at 11 59 PM Complete 71 Number Line L1 Substitution Level 2 Elimination Level 2 Question Watch Vic Find the solution of the system of equations x 4y 25 2x 2y 10

Algebra

Quadratic equationsGraph the following function by starting with the graph of y x and using transformations shifting compressing stretching and or reflection 12 f x x x X 4 Select all the transformations that are needed to graph the given function using y 1 A Compress the graph vertically by a factor of 2 9 B Shift the graph down units c Reflect the graph about the y axis 1 D Stretch the graph vertically by a factor of 2 E Shift the graph to the left 1 unit F Reflect the graph about the x axis G Shift the graph to the right 1 unit

Algebra

Quadratic equationsSiven f x 25x 10x 1 answer the following Graph the function Determine the domain and range of the function Determine where the function is increasing and where it is decreasing Graph the function Choose the correct graph below A B C A Q O D Determine the domain and range of the function The domain is 00 00 Tyno your answer in intonal notation Ico intogors or fractions for any numbers in the expression Heo a comma to coparato answers as poodod

Algebra

Quadratic equationsGraph the function f x x 8x 11 by starting with the graph of y x and using transformations shifting stretching compressing and or reflecting Select all the transformations needed to graph the given function using y x A Compress the graph vertically by a factor of 5 B Shift the graph up 5 units C Reflect the graph about the y axis D Shift the graph down 5 units E Shift the graph to the right 4 units F Reflect the graph about the x axis G Stretch the graph vertically by a factor of 8 H Shift the graph to the left 4 units

Algebra

Quadratic equations2 2 Complete parts a d for the functions f x x 5x and g x x 3x 4 Q W b Solve f x g x The solution set is 2 1 Use a comma to separate answers as needed c Use the result of part b to label the points of intersection of the graphs off and g The points of intersection are W

Algebra

Quadratic equations2 Complete parts a d for the functions f x x 5x and g x x 3x 4 a Graph f and g on the same Cartesian plane Choose the correct graph below O A O C IA b Solve f x g x The solution set is OB Q D

Algebra

Quadratic equationsSuppose that f x x 6x 5 A What is the vertex of f B What are the x intercepts of the graph of f C Solve f x 5 for x What points are on the graph of f D Use the information obtained in parts A C to graph f x x 6x 5 A The vertex off is Type an ordered pair

Algebra

Quadratic equationsGiven f x 25x 10x 1 answer the following a Graph the function b Determine the domain and range of the function c Determine where the function is increasing and where it is decreasing a Graph the function Choose the correct graph below O A O B Q O C Q O D

Algebra

Quadratic equationsClick here to watch the video 2 Why does the function f x 3x 12x 5 have two x intercepts Choose the correct answer below O A 2 There are two x intercepts because b 4ac 0 2 2 OB There are two x intercepts because b 4ac 0 OC There are two x intercepts because b 4ac 0 OD There are two x intercepts because b 4ac 0 2

Algebra

Quadratic equations3 A recipe for pie calls for 3 cups of butter for every two cups of flour If you follow the recipe and use 5 cups of flour how much butter will you need a 4 b 4 5 c 6 d 6 75 e 7 5 4 Mike makes 3 shots for every 5 he takes If he takes 60 shots one practice how many times will he miss a 24 c 36 e 100 b 28 d 40

Algebra

Quadratic equationsSamantha invests 555 in an account that earns 14 interest compounded continuously When will the value of the investment reach 1400 Graph the function on a graphing calculator or a desmos com and use the graph to make the prediction

Algebra

Quadratic equationsa Graph the following function using transformations b Find the real zeros of the function c Determine the x intercepts on the graph of the function f x 4 x 5 4 b What are the zeros of the function Simplify your answer Use a comma to separate answers as needed c What are the x intercepts 18 16 44 124 40 g 8 1614 12 10 81 6 4 22 do on No 46 12 1618 10

Algebra

Quadratic equationsDetermine whether 1 2 is a solution of the system 3x 2y 5 x 3y 10 Is 1 2 a solution of the system Choose the correct answer below O Yes O No

Algebra

Quadratic equationsa Graph the following function using transformations b Find the real zeros of the function c Determine the x intercepts on the graph of the function f x 4 x 3 16 b What are the zeros of the function Simplify your answer Use a comma to separate answers as needed c What are the x intercepts ID 18 he 44 142 40 6 18 1614 12 10 81 6 4 22 10 12 Y 4 6 8 11101

Algebra

Quadratic equationsMath 120 2 8 pts a Use the graph of y f x shown in the figure to sketch the graph of y f x Plot at least three points on the graph of f and the line given by y x b What are the domain and range of f and f 1 0 3 12 pts The function f x x 2 is not one to one a Restrict its domain so that the restricted function is one to one There is more than one correct answer b Find the inverse of the function with your restricted domain c Graph the domain restricted function and its inverse on the grid below Show at least three points on each graph d What are the domain and range of the restricted f and its inverse f

Algebra

Quadratic equationsopen box is to be constructed from a square sheet of metal with dimensions x feet by x feet by removing a square side 1 foot from each corner and turning up the edges The volume V of the box is V x x 2 Find the mensions of the sheet metal needed to make a box that will hold 144 cubic feet by solving the equation V x 144