Quadratic equations Questions and Answers

Which of the following is equivalent to the expression below Select all that apply 27y zu log3 3 log y 4log z 4 log u log 27y log zu 3 logg y loga z 4log u log 27y 4 log zu 3 logg y log3 z 4log u

a Evaluate log4 256 without a calculator b Which of the following is equivalent to log4 256 using the change of base property Select all that apply In 4 In 256 log 4 log 256 log 256 log 4 log256 4 In 256 In 4 c Use a calculator on your correct answers from part b Are the answers from part a and part b equivalent O Yes

Let x y z be non zero vectors and suppose w 18x18y 4z If z 3x 3y then w Using the calculation above mark the statements below that must be true A Span w x y Span y z B Span w z Span w x C Span w x Span w y D Span w x y Span w z r 6 x 6 y

Rewrite the following logarithmic expression as one logarithm 9 ln x ln y 16 ln z

Which of the following is equivalent to the expression below Select all that apply logs x7 7 logs x logs logs x 7log x

Which of the following is equivalent to the expression below Select all that apply logis cy log18 x log18 Y logis 2 logis y log18 2 log18 y

Suppose the roots of a Show that r r2 quadratic equation ax bx c 0 are r and r2 b and r r2 in two different ways a a

Which of the following is equivalent to the expression below Select all that apply log22 y log22 2 log22 y log22 2 log22 y log22 2 logan y loga z log22

5 5 2 v 24 A 2urv R 0 D 1 6 6 21 2 A 16x B D 16pl2

Divide using synthetic division x5 4x 3x 5x 12x 4 x 3 x5 4x 3x 5x 12x 4 x 3 Simplify your answer Use integers or fractions for any numbers in the expression Do

Find a quadratic function f whose graph matches the one in the figure f x 0 10 10 0 6 SU

What is the rule Select the correct choice below and fill in the answer boxes within your choice OA f x if xs if x OB f x if x if x2 3 2 R th 2 3

rewrite each fraction in terms of the LCD 1 5x 1 x 2 5x 5x 1 x 3

Simplify the given expression 3 3 VY

Simplify the given expression 5 5

Subtract x x 3 x 3x 5 x 2x 8 x 2x 8 O O O O 2 x 2 2x 2 x 2x 8 2 x 4 1 x 1

Solve for x x 3 x 3 O2 O 2 D 4

Simplify 5 x 6x x 2 Enter your answer in the b

Simplify x 4x 3 2x 1 2 x x 2x2 3x 1 O O x 3 x 1 x 2x 1 x 3 x x 1 x 3 x 1 I x 3 x 1 2x 1

Add x 1 X O O O x 55 x 4x 2x 1 x x 1 T 1 r T 1 I 3x 1 x x 1 22 1 T T 1

Add x 2 52 4 9x2 1 9x 1 O x 2 3xz 1 6x 2 3x 1 2 3x 1 4x 2 97 1

Solve for x 2 x 4 O 1 1 x 2 32 1 2 3 x 2

Which domain restrictions apply to this rational expression x 4x 4 x 4 Select each correct answer O x 4 x 2 0 x 0 0 x 2 C E

x 5x 24 x 0x 0x 8

2m n 2m n 2mm A 16m n 9 4n B D 14 512m 6 120 10 10 A C 2a 2a 2a b 46 2 B 16ba D 4a17

After declining between 1940 and 1980 the number of multigenerational households has been increasing since 1980 The function h x 0 012x 0 573x 35 726 can b used to estimate the number of multigenerational households in country A in millions x years after 1940 In what year were there 40 million multigenerational households There were 40 million multigenerational households in Round down to the nearest whole number

Use the quadratic formula to find exact solutions 8x 4x 5 X Simplify your answer Type your answer in the form a bi Use a comma to separate answers as needed Use integers or fractions for any numbers in t

ve for x X 1 0 The solution is x 0 Simplify your answer Type an exact answer using ra Express complex numbers in terms of i Use a comma as needed

Cool Down Find Some Find all points of intersection between the graphs of the functions f x x 5 x and g x x 5

Let the function P be defined by P x x 10x 23x 132 where x 11 is a factor To rewrite the function as the product of two factors long division was used but an error was made 1 Identify the error x 21x 208 x 11 x 10x 23x 132 x 11x 2 Redo the long division correctly 21x 23x 21x 231x 208x132 208x 2288 2156

P is a polynomial defined by P x 4x 11x 6x 9 Two factors are x 1 Rewrite the expression for P as the product of linear factors Here is a blank diagram to use to organize your thinking if needed

The equation A t 8000e0 06t gives the balance after t years of an initial investment of 8000 dollars which pays 6 00 compounded continuously dA a Find a formula for dt b Find and interpret A 6 Include appropriate units c Compare the approximation of 688 to the actual change Report your answer to two decimal places a dA dt b A 6 Round up to the nearest dollar Interpret A 6 688 OA The future value of a 7 year investment of 8001 will be of 8000 B The future value of a 6 year investment of 8001 will be of 8000 more than the future value of a 6 year investment more than the future value of a 6 year investment OC The future value of a 6 year investment of 8000 at 7 00 will be investment of 8000 at 6 00 OD The future value of a 7 year investment of 8000 will be more than the future value of a 6 year more than the future value of a 6 year investment

Find the amount of each payment into a sinking fund if 15000 must be accumulated Payments are made at the end of each quarter for 3 years with interest of 6 compounded quarterly Round to the nearest cent

3 5 Simplify Your answer should contain only positive exponents 11 a 4 12 12 4k A 16a A k 2 C 1 C 13 1 256a4 15 3 3 3 2v 4v A 4p 1 B B 1 D 3 B 4 D 2v 14 16 4 4 A 4 4 C 4 14 16 A B 64k D 16k 13 17 B B 3 x 2

Simplify 9 2p4 A p C 9p 12 B p 2 D 4p 10 10 3v 4 A 16v8 C v6 B 16 2 D 81v4

Exercise 4 Find complex solutions of the follow ing equations Hint assume z a bi where a b R 1 z z 1 0 2 z 2iz 5 0 3 24 3iz 4 0 4 3z 5iz 2 0 5 422 9 0

392n A 8n 3 B 16 2n

Simplify 48r A 8r 3 B 6 3 C 4r 3

Simplify 245 PO

Simplify 4864 C 2 5 6 7 8

8 A 1 1

Simplify the expression 2 xo QC X

Find two functions f and g such that h x can be expressed as the function indicated Several answers are possib h x 3x x f g f x g x

5 Simplify 5 2b ba 2a b A 4b a C 4a b 77 3v 20 v A 9 B 16ba D 48 B Simplify Your answer should contain only positive exponents 8 12 S 6 D 4v 6 451 2 A 6y x 8 A 4x 02 B 24x D 8x 12 2 B D

rite the expression as a function of x with no angle measure involved sin TO 4 X 1 cos x sinx 2 mplify your answer including any radicals Use integers or fractions for any numbers in the expressi

Use identities to find values of the sine and cosine functions of the function for the angle measure 7 3 20 given sin Question 8 5 5 11 Part 1 of 2 and cos 0 0 cos 20 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

Question 4 5 5 37 Use a double angle identity to find the exact value of the expression cos 2120 sin 2120 cos 2120 sin2 120 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

Find the zero s of the following function x x 14x 4 The zero s of the function is are Simplify your answer including any radicals Usent numbers in the expression Use a comma to separate Express complex numbers in terms of i Type each m

Find the zero s of the following function f w w 10w 21 The zero s of the function is are Simplify your answer including any radicals Use integers or fe numbers in the expression Use a comma to separate answers Express complex numbers in terms of i Type each solution of

7 9 points Given the polynomial p x x x 1 x 5 do the following a Determine all of the x intercepts of the graph of p x X b For each x intercept found in a give the multiplicity of each AND then tell whether the graph CROSSES or TOUCHES TURNS at each of the x intercepts answer both for each intercept