Quadratic equations Questions and Answers

b c 3 5ab3 Write your answer using only positive exponents 0 15a

3 Lydia is deciding which company she should hire to clean her carpet Company A 140 plus an extra 15 off Company B 0 50 per square foot Company C 42 50 per room 0 50 11 62 Lydia has 3 rooms to clean Each room is 8 feet by 11 feet Which company offers Lydia the best price Show your work and explain how you found your answer

2 Derrick went to the grocery store and purchased of a pound of ham for 6 99 per pound of a pound of cheese for 3 99 p r pound a loaf of bread for 2 49 and 1 gallon of milk for 2 89 The sales tax on food items in his tate is 4 3 What is Derrick s total for the groceries 544 after tax Round your answer to the nearest cent Sub total

17 Which values of x satisfy the inequality 2x 3 11 a X 4 B x 4 c X 4 d X 4

7 Without solving identify whether each of the following equations has a unique solution no solution or infinitely many solutions a 3x 5 2 b 6 x 11 15 4x c 12x 9 8x 1 4x d 2 x 3 10x 6 8x e 5x 6 5x 4

11 If 2x 4 5 what is the value of 6x 3 a 0 b 0 5 c 4 5

a 3x 5 2 b 6 x 11 15 4x c 12x 9 8x 1 4x d 2 x 3 10x 6 8x e 5x 6 5x 4 8 If 21 12 what is the value of 4t 4 a 6 b 10 20 d 42 9 If kand k 5 what is the value of x a 4 5 b 5 c 12 d 18 18 2 5 4

4 Debbie s employee has reached her 1 year anniversary with the company and gets a 10 raise The employee used to earn 15 00 per hour How much does the employee earn in a 40 hour week with the 10 raise a 540 00 b 600 00 c 606 00 d 660 00

c d 3 2x50 1 2 28 2

2 1 x sy b 3 y 1 4 x 1 lo

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What is the range for the quadratic 2 function y x 2x 3 Answer x 3 O y 2 O y 1 all real numbers

What is the axis of symmetry for the quadratic function y x 2x 3 2 Answer Additional Solution No Solution

What is the domain for the quadratic 2 function y x 2x 3 Answer x 3 Y 2 x 1 all real numbers Submit

What is the y intercept quadratic function y Answer 0 2 2 0 3 0 0 3 for the 2 x 2x 3

Factor Answer x 11x 24 2

Factor the expression completely 5x Answer X

Solve the following quadratic equation for all values of x in simplest form 4 x 9 20 Answer Additional Solution 4 No Solution

3 1 3 4 Factor each completely 1 8x 28x 3 Simplify each expression 2x x 3 A B C D 5 i 2x x 2 5x2 5x 6 2x x 3 4x 10x x 3 x 2 6x 3x x 1 2x 1 2x 3x 2 61 6 7 2 4 2 6x 4x 4 3x S A B C 7 D 2 4x 6 6x 5x 4 2 2x 3 6x 7x 1 2 2x 3 6x 9x 2 2 2x 3 3x 3 8 S P 500 trending up

What does this puzzle represent 1

2 Sketch the graph of the function below being sure to include at least two full periods y cos x 7 y X

5 Determine whether the function below is even odd or neither f x 3secx Odd Neither

3 Find the relationship between the graphs of fand g Consider amplitude period and shifts f x sin 9x g x 4 sin 9x g is a shift of f9 units downward Og is a shift of f4 units downward g is a shift of f4 units upward The period of g is 4 times the period of f

11 Let W be the subspace of R spanned by the vectors v 0 1 0 1 and v 1 0 1 0 Find the orthogonal projection of b 1 2 1 1 onto W a 1 1 1 b 3 2 1 1 c 1 1 1 d 1 0 1 0 1 27

14 Which of the following statements are always true i The set of nonzero rows of a matrix A is a basis for the row space of A ii If R is the reduced row echelon form of A then the columns of R with leading I s forms basis for the column space of A iii If E is an elementary matrix then the matrices A and EA have the same row space a all of them b none of them e i and ii only d iii only e i and iii only

7 The displacement from equilibrium of an oscillating weight suspended by a spring and subject to the damping effect of friction is given by All changes saved y 2e cos 6t 1 where y is the displacement in centimeters and t is the time in seconds see figure Find the displacement when t 4 Round your answer two decimal places

6 The displacement from equilibrium of an oscillating weight suspended by a spring is given by 1 y 2cos 6t where y is the displacement in centimeters and t is the time in seconds see figure Find the displacement when t answers to two decimal places 4 A 3 2 wwwwww Equilibrium Displacement Round yo

10 A 20 meter line is used to tether a helium filled balloon Because of a breeze the line makes an angle of approximately 85 with the ground Use a trigonometric function to write an equation involving the unknown quantity and explain what you did to set this up and solve

f x is a one to one function How many x intercepts Extra Credit Suppose y can the graph of the function f 1 inverse of the function f x have Explain your answer

3 Will Barrow wanted to know how tall the flagpole was in front of his school To find its height he drove a stake into the ground at the tip of flagpole s shadow and recorded the angle of elevation at two different times during the day He then measured the distance between the stake Will s data is below Stake A B Distance between stakes A B Time 2 00 PM 3 00 PM 12 feet Angle of Elevation 80 59

6 Conside the following piece wise function x 2 if x 0 e llestradogle onlinresis a if 0 x 2 4 if x 2 a Calculate the following values f 3 f 2 and f 1 f x x 2 PIGI b Graph the piece wise function Use the grid provided below N 5 4 3 2 1 5 4 3 2 1 tyd habbom si absti mill c State the domain and range of f x 1 2 3 4 5 90097 Hib ade brid ch I 2 3 4 5 under of

9 Using properties of logarithms express log c 5 rithms as a s

10 Find the point x y on the unit circle that corresponds to the real number t 57 How did you find that

7 Evaluate if possible the sine cosine and tangent of the real number 7

1 y x 6x 9x 1 find I

ABEN AB 6 A B A B

e the system of equations 2x y 5 and 3x 4y 42 by ations try 5 4y 42 2x y 3x 4y 2x Y 3x 4y x y ANABANG 5 42

Determine whether this is a parabola x 2y 12y 9 O Parabola O Not a parabola If it is a parabola write the equation in standard form y k 4p x h or x h 4p y k Otherwise leave the rest blank h k P p

Answer Attempt 1 out of 2 Watch Video Question Members of a softball team raised 1525 50 to go to a tournament They rented a bus for 1075 50 and budgeted 37 50 per player for meals Write and solve an equation which can be used to determine x the number of players the team can bring to the tournament Equation Show Example

REVIEW Simplify each difference 1 1 4 2n n 3 6n 2n A 3n 4n 1 B 3n 19n 1 C 3m 16n 1 D 3n 8m 1 Simplify each sum 2 4x 6x 4r 3r A 10x 2x C 5x B 10x D 3x

E 16 17 18 E Evaluate each function ANSWER SHOULD BE A FRACTION OR MIXED NUMB ANSWERS GIVEN AS A DECINMAL WILL BE COUNTED AS INCORRECT 5 Mx x Find Solve each inequality 6 57m 1 6211 A 7 2 B 7 orm 2 C 2005 D 20 or 5 4 O Solve each inequality and graph its solution 7 3 2 4 4 45 A ke 1 ork 7 B 7 4 7 C 5 or 7 D 7 5 DO zoom in

REVIEW 2 Final Sum REVIEW Write the point slope form of the equation of the line through the given points 12 through 0 3 and 2 1 13 A y 3 x 3 B y 4 x 3 D j x 3 Evaluate each function 2 h x x 4x Find M 10 B S D 140 A 32 C 4 Evaluate each function Round to the nearest hundredth if necessary TWO DIGITS

Solve the following system of equations There is a unique solution which should be entered as the ordered triplet x y z 2x 5y z 25 4x4z 24 6x 15y 3x 27

in the figure below a 10 b 11 and c 14 Use this information to solve the parallelogram for 0 The diagonals of the parallelogram are represented by c and d Round your answer to two decimal places C b a 8 P

0 Give the three formulas for the law of cosines and explain how you use the Law of Cosines Also tell which congruence cases use Law of Cosines and which use Law of Sines ex SAS SSS

2 Use the low of Cosines to solve the given triangle Round your answer to two decimal places a 54 b 24 c 71 0 A 126 69 B 15 73 C 37 58 0 A 37 58 B 126 69 C 15 73 0 A 126 69 B 37 58 C 15 73 0 A 37 58 B 15 73 C 126 69 1 15 720 R 27 500 126 60

5 Use the Heron s formula to find the area of the triangle Round your answer upto two decimal pla a 12 42 b 8 56 c 15 15 29 44 12 51

5 Select a value for b such that a triangle with A 33 and a 4 has no soluti A A 3 67 14 68 1 84 O 1 47 7 24

6 Use the figure below to determine the exact value of the given function csc 20 2 8

6 5 4 3 2 1 7 6 5 4 3 2 41 1 2 3 Slope m 7 6 7 1 Find the slope of the line 2 3 4 5 6