Quadratic equations Questions and Answers

What 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

Given 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

6 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

3 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

SA 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

Enter 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

3 57 7z 2x 8xz 4r 11 0 Find all the zeros for each function

5 3 5 9 4 6

Reduce the fraction 180 100

Add 28 782 5 188 16 542

Algebra 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

19 y x 5 x 2 Use a graphing calculator to find the r

15 x 2 1 4 Find the zeros of each function State the multiplicity

Find the slope and y intercept of the line whose equation is 2x 11y 55

Q1 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

Factor 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

A 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

A 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

The 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

logs 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

Select 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

Graph 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

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

Find the equation of the line through 2 3 and parallel to 3x 5y 10

4 Find the equation of the line with x intercept 4 and y intercept 3

Given 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

Let 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

y 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

a 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

Marcus 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

A 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

Find 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

At 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

Complete 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

M1 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

Graph 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

Siven 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

Graph 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

2 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

2 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

Suppose 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

Given 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

Click 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

3 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

Samantha 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

a 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

Determine 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

a 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

Math 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

open 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