Quadratic equations Questions and Answers

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

neither even nor odd is even odd or Is this function even odd or neither even nor odd OA Neither even nor odd OB Odd OC Even W 10 X 20

10 Point A is the incenter of AFGH Find AS A B C D 5 324w 0 in

Tony is using a triangular prism to make the top of a toy house He wants to know how much cardboard he needs to build the roof Indicate whether the information in the first column is necessary or not necessary in order to make this decisi Information The number of edges The area of each triangle The length of each rectangle The number of faces Necessary Not Necessary

x a x c Let r x Find a c and n such that the graph of r x has all of the following properties no vertical asymptotes x intercept 5 0 horizontal asymptote y 0 and y intercept 0 1 2 Drag and drop the answers from the given set below 5 10 0 5 any even number any whole number 1 not possible 1

The function g x shown in the table below is a linear function Find its slope y intercept and formula in stope intercept form g x The slope is The y intercept is The slope intercept form is a z 12 63 09 00 8 4 23 43 WID 3 4 B 12 17 37 57 16 20 17 97

The formula of the radius r of a sphere with surface area A is re A Rationalize the denominator of the radical expression in this formula Type an exact answer using as needed Type an exact appa

Jane owns a bakery and she wishes to apply quantitative modelling to her small business She estimates that the demand for her pullman loaves can be defined as in the following d x 2be where b 0 and is a constant Given that the loaves sell at price x pesos formulate an optimization model that would allow her to maximize her revenue At what selling price of the loaves will the optimal revenue be achieved Selling Price Given the optimal selling price how much revenue should Jane expect to receive round off to 4 decimal places Optimal Revenue

10 8 6 1 10 Equation 5 5 10 6 8 10 Write the equation of the line shown Be sure to use the correct variable

uses see image Answer the question about the following graph List of du path for variable x 0 1 7 0 1 2 4 5 3 2 4 5 3 2 4 6 1 7 3 2 4 5 6 1 7 4pt Specify the set of du path to satisfy all def coverage with respect to x 4pt Specify the set of du path to satisfy all uses coverage with respect to x

Write loga2 12loga3 2loga5loga2 12loga3 2loga5 as the logarithm of a single value with base a Show the steps

et X Y and Z be sets prove that Xn YAZ XY A XnZ

A pyramid was built about 2600 BC Its original height was 586 feet 7 inches but due to loss of its topmost stones it is now shorter Find the current height of the pyramid using the information given in the figure on the right The current height of the pyramid is feet Do not round until the final answer Then round to two decimal places as needed 41 90 48 48 125 At 250 ft

A rectangular field with base x and height 2r is surmounted by two semicircular fields as shown in the diagram below The external perimeter of the fields solid blue track is 200 meters Answer the following a Express the area A of the rectangular field shaded green as a function of r A r b Determine the maximum area enclosed by the rectangular field Type pl if you need it or look in the MathPad Gre list Decimal approximations are marked incorrect Maximum area square meters X

The exponential function given by H t 80 039 77 1 0482 where t is the number of years after 1995 can be used to project the number of centenarians in a certain country Use this function to project the centenarian population in this country in 1998 and in 2027 The centenarian population in 1998 is approximately 92180 Round to the nearest whole number The centenarian population in 2027 is approximately Round to the nearest whole number

Sketch the graph of the following function Describe how the graph can be obtained from the graph of the basic exponential function 2 f x 2 3 m Use the graphing tool to graph the equation Click to enlarge graph Ay 10 8 8 42 46 x A

State the base of the exponent 7 in the expression p 5 7 The base of the exponent 7 is

Use the graphing tool to graph the equation Use the intercepts when drawing and another point to draw the line Click to enlarge graph B 5 N 8 ob T

Evaluate each of the following using the laws of logarithms Show all steps and final answers must be displayed as a whole number a log2 24 3log2 2 log2 6 b 5 log5 1 5 2log5 5

Use the graphs if necessary of the functions to the right If g 5 35 write the corresponding ordered pair Z SA X 10 10 HIS H 10

Simplify Choose all that apply to the answer 14 203 125 Select one or more O a There is an even number outside the radical b There is an odd number under the radical c There is an odd number outside the radical Od There is an even number under the radical

Problem25 In triangle ABC XY AB such that the area of triangle CXY is equal to the area of trapezoid ABYX CP is an altitude of triangle ABC What is the ratio CQ CP C 1 D 2 A 1 2 B 1 2 AAS KON E 2 C AAS AM X Q Y

Od There is an even number outside the radical Check What is the value in the denominator after you rationalize the denominator 4 3 3 2

26 Guillermo has sold 87 33 118 and 70 appliances in the last four months respectively How many appliances will he need to sell this month to maintain an average of at least 75 sales per month answer

At 2 00 p m there are 350 freshmen and 200 sophomores at a school carnival After 2 00 p m 20 freshmen leave every half hour and 35 sophomores arrive every half hour What is the ratio of freshmen to sophomores at 4 00 p m in fraction form

etermine the x and y values of the solution of the system ate your answers as decimals not fractions y

29 Considering the inequality 5x 4y 12 the shaded area of its graph is described by O shaded above a dashed line shaded above a solid line shaded below a dashed line shaded below a solid line

3 Solve the linear systems of equations using the elimina addition multiplication method 10x 10y 80 13x 6y 83 x 6 y 1 x 6 y 4 x 5 y 3 x 5 y 2

1 Solve the inequality set Graph the solution on a nu x 4 0 and x 11 11 O x 4 and x 0 O x 4 and x 0 O x 0 O x 4 O all real numbers

3 Solve the systems of linear equations using a graphing method 15x 3y 99 y 5x 33 O 2 6 O 5 2 6 3

14 Solve the inequality set Graph the solution on a nu x 3 6 and x 2 3 O x 1 and x 3 0 x 1 O x 1 and x 3 O x 3 O all real numbers no solution

6 Choose the name of the linear equation form given 2x 7 O not a linear equation O slope intercept form O standard form O none of the above

and or subtraction with multiplication method Select the best answer with the format x y 4x y 21 4x 5y 63 O 7 7 O 13 12 O 1 16 O 9 10 no solution infinite solutions 18 Convert the following equation to its alternate form standard to slope intercept or vice versa 3x y 9

Graph the following system on a sheet of paper or graphi 5 and y 3 which of the following points if any satisfy t More than one answer may be correct check all correct a 3 3 6 9 6 6 1 2 5 6 4 9 3 3 Determine None of these points satisfy the system

3 For the following quadratic function identify the st which are true Check all correct statements y 4 x 2 Hint Notice there is no k so k 0 Direction opens down Coordinates of Vertex 2 0 Vertex is a maximum y intercept 16 Equation of Line of Symmetry 2

For the following quadratic function identify the stat which are true Check all correct statements y 2x 4x Hint Notice there is no constant term s0 C o c 0 Line of Symmetry x 2 Direction opens up y intercept 0 Vertex is a maximum

12 Which term is the linear term in the equation y 3x 12x 18 O 12x 3x O 12 18

For the following quadratic function identify the stater which are true Check all correct statements x 2x 2 Equation of Line of Symmetry x 1 y intercept 4 Vertex is a maximum Coordinates of Vertex 1 1 Direction opens down

Find the y intercept and state whether the graph opens up or down y 4 x 3 9 More than one answer may be correct check all that y intercept 45 Direction or opening down 42 y intercept Oy intercept 47 Direction or opening up

2 Convert the following to standard form then write the quadratic term the linear term and the constant term in the space provided x x 1 Quadratic term Linear term Constant term

the constant term f x 5x 6 Quadratic term Linear term Constant term 8 5 Identify the line of symmetry of the parabola defined b y 4 x 8 6 x 5 O x 6 O x 6 x

The graph of y f x is given Graph the function y f x 2 1 3 2 7 3 2 AP 2 3 4 y f x

Using the dist lant state th of solutions for the following equation Hint express your answer as an integer 0 1 2 or 5x 10x 5 Number of solutions 1 For the following equation Find the value of the discriminant z 3z 6 Discriminant 5 For the following equation Decide how many different real number roots the equation has a 4a 4 different real number root s

Using the discriminant state the number of solutions for the following equation Hint express your answer as an integer 0 1 2 or 3 z 8z 16 Number of solutions Using the discriminant state the number of solutions for the following equation Hint express your answer as an integer 0 1 2 or 3 5x 10x 5

t 26 t O 5 17 O 15 18 O 5 10 O 5 06 13 Solve the following equation using the quadratic formula 2x 2 149x 0 821 0 O 3 339 2 345 and 6 169 0 267 and 4 494 O 1 422 O 1 652 and 0 497

7 Solve the following equation using the quadratic formula x 14x 49 0 O 11 0 7 O 12 07 O 5 O This quadratic has no solution

1 Solve the following by taking the square root 4c 44 Round your answer to the nearest hundredth c

9 Identify the solutions to the equation 4x 12x 9 when you solve by completing the square O X 3 2 O X O O No real solutions X 3 2 32 or x 10 Identify the solutions to the equation x 5x 50 when you solve by completing the square X 5 or x 10 O x 5 or x 10 Ox 0 x 5 or x 5 or x 32 10 10 No real solutions