Quadratic equations Questions and Answers

For the functions f x 3x 6 and g x 3 fg x would be equal to a fg x x 2 Ob fg x 3x 3 c fg x 9r 18 d fg x 9x 18

Is the relation in the table a function X 23 27 19 32 55 y 15 14 16 15 19 No One input value has more than one output value Yes Each output value corresponds to only one input value Yes Each input value corresponds to only one output value 3 of 10 QUESTIONS

Homework Unit 7 MATH 0307 14 1 1 ordered pair solutions Determine whether each ordered pair is a solution of the system of linear equations 3x y 7 x 9y 21 a 3 2 b 4 5 a Is 3 2 a solution Yes No b Is 4 5 a solution O No

1 Use the graph below to help you answer the questions Y 40 X 68 a Show use of division to find the remaining roots of y x 4x x 4 b Use the roots to rewrite the function in factored form c Classify the original polynomial by its degree and number of terms d Describe end behavior turning points and increasing decreasing intervals of the graph 2 The data in the table

Terminal point 0 3 5 4 3 u 5 3 1 A N L 2 3 4 13 61 1 2 3 4 5 Initial point 0 0 Initial point 3 3 termine if the vectors given in the figure above are equal

Plot the ordered pair 1 1 State in which quadrant or on which axis the point lies Plot the ordered pair on the graph to the right In which quadrant or on which axis does the point lie O III O O IV O O OI on the y axis on the x axis 10

Find the polynomial of degree 4 whose graph goes through the points 2 49 1 3 0 3 1 11 and 3 39 f x 3x 4 4x 3 5x 2 4x 8

Find a cubic and a quartic model for the set of values below Then determine which model best represents the values 2 1 0 1 2 57 20 5 13 X y 98 The cubic model is f x x 0x x O Simplify your answer Type integers or decimals Round to three decimal places as needed

Revenue Growth Suppose that the annual revenue R in millions of dollars of a company after t years of operating is modeled by the function R 1 2

The image of A 1 3 under the translation T2 1 is

Which inequality is graphed below 7 6 5 0x212 Ox 2 Ox 2 3 2 1 0 2 3 S

1 5 R 5 The data in the table shows the times for Men s 500 m Speed Skating event at the Winter Olympics Let x be the number of years since 1980 Year 1984 1988 1992 1994 1998 2002 2006 Time sec 38 19 36 45 37 14 36 33 35 59 34 42 34 84 SOURCE www infoplease com a Find a quadratic model for the data set b Find a cubic model for the data set c Find a quartic model for the data set d Compare the models and determine which one is more appropriate Explain your choice Submission status

14 Use the graphs of f x solid line and g x dashed line below to answer the parts that follow g x a 4 points Use the graphs above to complete the table below f x g x fg x O x 0 1 2 3 f x 2 5 b 3 points Use the table completed in a to construct the graph of y g x on the grid above 3

point Use the graph of y g x given above to find a g 1 3 b g 2 1 c The domain d The range y g x 5 4 3 2 1 point The equation of the line that goes through the point 4 2 and is parallel to the line going through the points 1 6 and 5 6 can be written in the form y mx b where mis and bis

Use the graph of the function to find its domain and range Write the domain and range in interval notation Provide your answer below 8 7 30 40 6 5 4 3 2 1 8 7 6 5 4 3 2 1 0 1 1 2 Y 3 4 5 6 7 a 2 19 3 4 5 40 6 7 8

Consider the mapping T R2 R given by O yes O NO Is T a linear map practice the full justification QUESTION 6 0 0 0 2 y 3 T Consider the mapping T R2 R2 given by O Yes O NO Is T a linear map practice the full justification T 5 6

Solve the equation by applying the Quadratic Formula Select its solution set x 16x 510 Select an answer and submit For keyboard navigation use the up down arrow kays to select an answer S to b c a 8 205 8 205 8 13 8 13

MyLab and Mastering 4 B 2 6 4 2 0 2 Y 2 6 x Assignments Drag the points A and B so that the length AB is equal to d where d 7 5 748 6 Check Answer 3 Save Submit is equal to d g the points A and B so that the leng

Evaluate x y for x 10 and y 40 x y

2 For the set of data compare two models and determine which one best fits the data where x years after 1900 Year 1990 1995 2000 U S Homes Average Sale Price thousands S 149 158 207 a Which model seems more likely to represent each set of data over time Give a reason for your answer b Using your model estimate the average sale price of homes sold in the United States for 2020

5 Given the function f x 3 x 2 27 use technology to find the features outlined below 35 points 5 each a Vertex b Y intercept c Zeros d Domain e Range 1 f 2 g Solve f x 24

3 Determine angle B to the nearest degree Show all steps in proper form for full marks 17 m 55 15 m

Solve and graph the following systems of limeon 1 x 3x 6 y x 2 ii X Y 47 3 4x 2y 10

Find two polar coordinate representations for the rectangular coordinate point 3 3 3 one with r 0 and one with r 0 and both with 0 0 2T Must show detailed work

The first digit does lie In front of thine eye Assume these triangles are similar Like all questions regular Find the value of x Then move on to what s next 9 9 3 5 21 10 5 12 6 21

Write an equation for the function graphed below Q

1 Simplify with only positive exponents 4 y xz 2 3 xy z

Which polynomial has complex roots 1 i 2 and 1 i 2 A x 2x 3 B x 2x 3 C x 2x 3 D x 2x 3 Select one O a A O b B O c C O d D

2 The data shows the power generated by a wind turbine The x column gives the wind speed in meters per second The y column gives the power generated in kilowatts X 5 6 7 8 9 y 10 17 28 27 44 40 96 58 32 a What is the first differences of the y values b What are the second differences of the y values c When are the differences constant

3 1 olynomial unctions SR 5 Dints 3 1 olynomial unctions CR 5 Dints 3 2 olynomials near Factors nd Zeros 5 2 3 2 olynomials inear Factors nd Zeros MathXL 3 2 olynomials 15 18 7 Determine the real solutions of the 4th degree polynomial shown 3 2 1 td 4 3 2 1 0 2 4 1 2 3 4 5 Submission status X

32 2 2 3 32 2 32 2 x 3 32 4 44 3 3 222

You have a restaurant bill of 61 45 If you are laxed 8 and decide to tip your server 15 how much is your total a 75 65 b 75 89 c 76 32 d 76 67 Please select the best answer from the choices provided

a Next question Perform the operation and simplify the rational expression b X x 1 3x 3x x 4 x 14x 8 17x 20 X Get a similar question You can retry this c 2x 5x x 4 4 x x x x 3x 11x 6 x x 12

A player throws a basketball toward a hoop The basketball follows a parabolic path that can be modeled by the equation y 125x 1 83x 4 The table models the parabolic path of another basketball thrown from somewhere else on the court If the center of the hoop is at 12 8 will each ball pass through the hoop 00 X y No Yes 26 co 8 CO 8 Will the basketball that follows a parabolic path modeled by y 125x 1 83x 4 pass through the ho 14 14

44 Explain why the function y log x 4 doesn t have a y intercept

P1 What is the value of the sum S given by 1 1 log N log N A 1 log 100 S B log 100 C log100 N N log 100 D log 100

The table shows the relation between the speed of a car and its stopping distance Speed mi h Stopping Distance ft Answer 35 45 50 60 96 140 165 221 Use a quadratic function to model the data Use your model to predict the stopping distance for a car traveling a mi h Round to the nearest foot A car traveling 65 mi h will have a stopping distance of feet

Find the square 2x 6 a b O C Od 4x 12x 36 4x 8x 36 4x 36 4x 24x 36 Question 5 1 point Simplify the expression 7 6 7 O a 7 7 O b 5 7 O C 5 14 Od 714

Write the equation of the parabola in vertex form vertex 2 4 point 1 2 f x

Add the proper constant to the binomial so that the resulting trinomial is a perfect square Then factor the trinomial m 12m Add the proper constant to make a perfect square trinomial m 12m Type an integer or a simplified fraction

Use this graph to answer the questions a What are the x intercepts b What are the zeros a The x intercepts are 8 0 7 0 Use a comma to separate answers Type an ordered pair b The zeros are rate answers

Q using the Discriminant of the Quadratic equation How many real solutions from the Equation 2x 3x 4

Brianna has 34 m of fencing to build a three sided fence around a rectangular plot of land that sits on a riverbank The fourth side of the enclosure would be the river The area of the land is 140 square meters List each set of possible dimensions length and width of the field

x 1 Part 1 f x Assuming f is one to one find a formula for f x f x Part 2 Function composition Check your answer to part 1 using function composition f of x

L K Which can be proved OA AKPN AKQN OB 1 KP 5LN P OC KQ PN OD PN KM

Is the graph on the right the graph of a polynomial function Yes

Is y 14x 67 increasing or decreasing decreasing increasing

a The graph of yf x is shown Draw the graph of y 4 14 X 2 b The graph of yg x is shown Draw the graph of y 2g x PO X G

Solve each of the following for C Do not use any formula for inverse functions in Section 3 7 a sin 2 0 b tan 2 1

31 Use a rectangular contour to evaluate the integrals eax a b c 8 r oc 00 1 ebx 0 r x2 dx where b is real and 0 Re a b sinhax sinh 4ax dx dx cosh ax