Quadratic equations Questions and Answers

For a function to be even which of the following must be correct 1 a f x f a O b f x f x c f x f x d f x 1

a p 0 1 b p 1 0 c p 0 1 d p 1 0

What function is graphed below 10 9 8 7 6 5 27 5 4 3 2 1 2 3 4 Of x 5 Of x 1 2 3 4 Of x 3 Of x e 3 5 Of x 3 Of x 3 of 2 17 2 Of x 4

The function below has the form f x b k 5 4 to 9 8 7 6 5 3 2 1 2 1 J 2 1 2 Of x Which of the following functions is shown on the graph 2 3 Of x Of z 1 3 3 k Of x 3 3 Of x 3 1 Of x 3 2 Of x 3 Of x 3 2 Of x 2 1 3 2

From the following chart choose two of the four function pairs i Explain the meaning of y f h x ii Give a real life example of y f h x h x Milage is a function of time Consumption is a function of Velocity Earnings is a function of Time Cost is a function of Consumption f x Fuel Consumption is a function of Milage Cost is a function of Consumption Interest is a function of Earnings Interest is a function of Cost

Suppose a ship is sailing at a rate of 35 km h parallel to a straight shoreline The ship is 10 km from shore when it passes a lighthouse at 11 am 0 a Let k be the distance between the lighthouse and the ship Let d be the distance that the ship has travelled since 11 am Express k as a function of d and include a diagram b Express d as a function of t the time elapsed since 11 am c Find ko d What does this function represent

Does the composition of functions display the commutative property Give an example of each case to illustrate your answer

Given the functions f x 3 and g x 3 x and h x x 3 what composition of functions would result in the following a y 3 3 b y x 6x 6 c y 6 x

Simplify Express answers using exponents 4 2 3 34 3 1 T 4 3 x y xy

Write an equation for the polynomial graphed below 6 5 4 5 4 3 2 y x 1 3 322 2 3 4 5 6 3 4 5

Based on all of the information you have gathered about global warming you should now be able to clearly communicate your thoughts on the matter Although you will summarize your thoughts in your own words for this first draft essay you should often support your opinions by referring to the resources that you found during your research Just as the scientists who study global warming have varying opinions so will the students in your class Any conclusion can be valid as long as you support your conclusion with your research Now write an essay with a minimum of five full paragraphs that expresses your opinions and persuades your reader to feel the same way Try to organize your essay effectively so that it is focused on the ideas that are central to your argument Also try to maintain a formal tone that balances the persuasive nature of your argument with an objective nonbiased approach that makes your piece credible believable Be sure to a Use scientific reasoning to explain why your opinions are valid b Explain why opposing opinions and reasoning are not as convincing c Cite at least three excerpts or quotations from at least three different resources from your research that support your conclusions d Use mathematical data where appropriate

3 Which relation is not a function X 10 6 2 1 5 1 y 2 2 6 9 13 3x 2y 4 2 123 y 3 4 A B C X

1 The expression w4 36 is equivalent to 1 w 18 w 18 2 w 18 w 18 3 w 6 w 6 4 w 6 w 6

business owner receives a 5 000 loan with 13 interest charged at the end of each year write an expression to represent the amount owed in dollars after the given number of years of making no payments 5000 after 1 year after 2 years So E after t years 5000 3

3 Find the maximum value of Q x subject to the constraints xx 1 and xu 0 where u is a unit eigenvector corresponding to the greatest eigenvalue of the matrix of the quadratic form Q x 3x 9x 5x O A 3 B 5 C 9 D 0

a quadratic equation in standard form that has the characteristics listed below Then graph your equation When creating your equation be sure that it will fit on the graph provided 4 points opens upward has a y intercept at 0 5 2 wider than y x

The radius of a pulley is 98 mm Find the circumference of the pulley This is the amount of rope that passes through the pulley as it rotates exactly once Round your answer to the nearest whole number Do not type the units in the space below

5 The Violent Crime Rate in the U S per 100 000 inhabitants from 2004 to 2010 can be modeled by the quadratic function C t 4 31t2 16 2t 461 51 where t represents the years since 2004 data source https ucr fbi gov Show complete work for the questions below Write your answers in complete sentences a Find the Violent Crime Rate per 100 000 U S inhabitants in 2004 b Find the Violent Crime Rate per 100 000 U S inhabitants in 2008 c In what year was the Violent Crime Rate per 100 000 U S inhabitants be 470 d In what year was the Violent Crime Rate per 100 000 U S inhabitants a maximum

1 A golfer hits a golf ball The graph of H t below shows the height of the ball in feet after t seconds Round answers to two decimal places as needed All answers must include appropriate units of measure Height of Golf Ball feet 120 100 80 60 40 20 2 3 6 Time seconds a Interpret the meaning of the vertex in this situation Write your answer in a complete sentence b Interpret the meaning of the horizontal intercepts in this situation Write your answers in complete sentences c Determine the practical domain of this function Write your answer in interval notation d Determine the practical range of this function Write your answer in interval notation

10 8 6 4 What is the area of ADEF Area 2 square units 6 4 2 0 2 4 9 6 8 10 2 IN 4 6

Part A Solve the equation 5 x 2 6x 3x 14 and show your work 5 points Part B Use this list of properties to justify each step of your math work Justifications may be used more than once if needed 5 points Distributive Property Subtraction Property of Equality Combine Like Terms Multiplication Property of Equality Division Property of Equality Given 4

3 4h j k n j k 4h j k 4 b c a b 6 0 10 4 j k jh x 6 2z 4 8 v x y z xy

6 What are the x intercepts of f 1 1 0 and 6 0 2 2 0 and 3 0 3 1 0 and 6 0 4 2 0 and 3 0

14 A company is considering building a manufacturing plant They determine the weekly production cost at site A to be A x 3x while the production cost at site B is B x 8x 3 where x represents the number of products in hundreds and A x and B x are the production costs in hundreds of dollars 6 pts a Graph the production cost functions on the set of axes below and label them site A and site B Cost hundreds of dollars 50 t 40 30 20 y 10 1 3 4 X 2 Number of Products hundreds b State the positive value s of x for which the production costs at the two sites are equal c If the company plans on manufacturing 200 products per week which site should they use

13 A rocket is fired into the air and its shape can be represented by a parabola with the equation y 2x 12x where y is the height in feet and x is the time in seconds a Construct a table label the axes and graph the parabola over the interval 0 x 6 on the grid below 20 c What is the maximum height of the rocket 15 10 5 5 10 15 20 b Determine the number of seconds it takes for the rocket to reach its maximum height 6 pts d How much time elapsed from when the rocket was launched until it landed back on the ground

A polynomial function contains the factors x x 2 and x 5 Which graph s below could represent the graph of this function 1 I only 2 II only 3 I and III 4 I II and III 11 y n

7 A student correctly graphed the parabola shown below to solve a given quadratic equation What are the roots of the quadratic equation associated with this graph y X

5 How does the graph of g x x 3 2 compare to 1 The vertex of g x has moved to the left 3 units and up 2 units 2 The vertex of g x has moved to the right 3 units and up 2 units 3 The vertex of g x has moved to the left 3 units and down 2 units 4 The vertex of g x has moved to the right 3 units and down 2 units

11 Given the function f x 2x 8x 15 find the axis of symmetry and vertex algebraically 3 pts

9 The function h t 16t 144 represents the height h t in feet of an object from the ground at t seconds after it is dropped A realistic domain for this function is 1 3 t 3 2 0 3 3 0 h t 144 4 all real numbers

4 Keith determines the zeros of the function f x to be 6 and 5 What could be Keith s function 1 f x x 5 x 6 2 f x x 5 x 6 3 f x x 5 x 6 4 f x x 5 x 6 Subula 20

1 Which set of points model a quadratic function 1 2 2 1 4 0 6 1 8 2 10 2 2 3 1 2 0 1 1 0 2 1 3 2 4 1 3 0 1 1 5 2 25 4 2 5 1 0 0 3 1 4 2 3

2 Which point is not on the graph represented by y x 3x 6 1 6 12 2 4 2 3 2 4 4 3 6

1 Show that a the following transformation T 11 12 13 2x1 12 21 73 72 23 is a linear in the space R E use the function T to find b the image of v 2 3 1 and c the preimag of the w 4 1 1

Solve the following functions 10 322 1 13 62 36 2 11 3 5 14 27 m 2 49m s 12 4 8 x s 15 5n 25n

Ex3 Now let s look at how to graph the exponential function y 72 1 y CERE 10 4 6 6 5

12 Find the minimum number of iterations of the bisection method required to approximate the root of f x 275 1 in the interval 1 1 so that the error is less than or equal to 6 10 5

Determine the terms that are under the ink spots px qx r 2x nx 6 an HA at y 2 B Given the equation g x ay intercept of 6 determine the values of p q rand n if the equation has the following a VA at x 2 2 Determine all the necessary information in order to draw a graph for g x intercepts asymptotes and other related inform an x intercept of 3 2x4 6x 8x x3 x2 using domain

1 Categorize each of the scenarios patterns or functions into the table below by whether it represents linear or exponential change A y 2 E 5 5 5 5 1 X 0 1 2 3 y 1 5 25 125 Linear B 7x7x7x7x7 F y 1 05 J X O 1 2 3 y 50 75 100 125 C y 9x G You add 50 to your account every month K X O 1 2 Exponential 3 5 50 500 5000 D y 2x H The value of an investment doubles every decade L

Graph the image of parallelogram FGHI after the following sequence of transformations Translation 17 units down Rotation 90 counterclockwise around the origin Fo I 14 12 10 8 G H 14 12 10 8 6 4 2 6 4 2 2 4 6 8 Y 2 4 6 8 10

given f x x and g x 6 x 2 6 find the following expressions a fog 4 b gof 2 c fof 1 d gog 0

Solve the given equation 12000 6000 1 r 22 r Simplify your answer Type an integer or decimal rounded to the nearest hundredth as

What is the area of square WXYZ 10 8 6 Area Submit N W 4 2 square units 104 8 6 4 2 0 2 4 9 6 8 10 Y X 2 4 6 8

5 7 Area and perimeter in the coordinate plane II MHQ What is the perimeter of square DEFG E D 104 F G 10 8 6 4 2 Perimeter 8 units 6 4 2 0 2 4 6 8 2 S 10 Write your answer as an integer or as a decimal rounded to the nearest tent E 4 6 8 GA co A F X 10

What is the area of rectangle CDEF 10 Area CL 8 6 Submit 4 F 2 square units 104 8 6 4 2 0 2 4 6 8 1 0 D 2 4 E 6 00 8 10

Describe the transformations in each graph Sketch the graphs of the following functions by hand using transformations Show your work show how the transformations map from the base function to the transformed function for the graph in addition to listing the information Graph values from 0 x 2T a f x 3 sin x 1 b f x cos 2x 2

Volume of 10 cu ft and weighs 50 lb The second product s unit volume is it and it weighs 40 lb If the company s trucks have 2 320 cu ft of space and can carry 21 600 lb how many units of each product can be transported in a single shipment with one truck using the entire volume and weight capacity first product second product Need Help Read It 9 2 Points DETAILS HARMATHAP12 1 5 040 MY NOTES ASK YOUR TEACHER A cake manufacturer boxes Swiss chocolate and German chocolate cakes at one site A box of Swiss chocolate cake contains 0 55 lb of a sugar mixture and 0 45 lb of flour A box of German chocolate cake contains 0 51 lb of the sugar mixture and 0 49 lb of flour Each day at this site the company has available 2 100 lb of the

1 find the x and y intercepts 2 find the domain and range 3 find the intervals of increasing decreasing and constant 4 Find the local maximum and minimum values and at what X value they occur S

A tube with one end closed has a second resonant frequency of 3187 5 Hz The length is increased by a factor of 4 Find the new second resonant frequency Show all work

Which two triangles are congruent b the ASA Theorem Complete the congruence statement Q A R PK J U