Quadratic equations Questions and Answers

1 y 4x 8x 3

9 6x 5x4

10 10x 19x 6

3 f x x 4x 4

7 8x 10x 3

2 100x

2 y x 16

8 9x 49

6 36x2 25

4 6x 17x

3 n 4 2 n 1 n n 3 2n

B 5 9 Solving Rational Expressions Solve each equation Remember to check for extraneous solutions 1 5 1 5 a 3a n 4 2 n 7 1 1 6 3 6 P P a 5 3a 1 n 3 n 2n 1 x 4 2 x 4 n 6 8 2 2 2 4 8 10 2 V 1 36 b 2r 1 2b 8b 1 v 5 1 1 2 2b 6 V 1 b 2 b 4 3r 3 10r n 5 n 4 b 5 b 4b

2 r 7r 8

8 56 13b 28

6 Sp 18p 8

4 x 49

2 1 m 17m 72

2 3a2 24a 45

7 y 3x 24x 27

4 14y2 7y 21

10 Find the vertex of y x 16x S

3 3x 31x 36

9 Find the product x 2 2x 7

7 y 3x 24x 27

6 2x 8

1 5t 5t

12 x y EN 60 x y 52 A 120 min x y B 136 C 142 D 156 E 172 The right right answer

2 Each day a local dog shelter spends an average of 2 40 on food per dog The manager estimates the shelter s daily expenses assuming there is at least one dog in the shelter using the function E x 30 2 40x Which statements regarding the function E x are correct I x represents the number of dogs at the shelter per day II x represents the number of volunteers at the shelter per day III 30 represents the shelter s total expenses per day IV 30 represents the shelter s nonfood expenses per day 1 I and III 2 I and IV 3 II and III 4 II and IV

4 When written in standard form the product of 3 x and 2x 5 is 2 2x 11x 15 4 6x 15 2x 5x 1 3x 2 3 2x x 15

5 David wanted to go on an amusement park ride A sign posted at the entrance read You must be greater than 42 inches tall and no more than 57 inches tall for this ride Which inequality would model the height x required for this amusement park ride 1 42 x 57 2 42 x 57 3 42 x or x 57 4 42 x or x 57

6 The table below shows the height in feet h t of a hot air balloon and the number of minutes t the balloon is in the air Time min Height ft 2 5 7 10 12 64 168 222 318 369 The function h t 30 5t 8 7 can be used to model this data table Explain the meaning of the slope in the context of the problem Explain the meaning of the y intercept in the context of the problem

8 Determine if the point 0 4 is a solution to the system of inequalities below Justify your answer 101 10 yz 2x 4

Show that In x x 1 for all x 1

Fill in the blanks to factor the trinomial 3x 13x 10 by grouping 3x 13x 10 3x x 3x 2 x 10 3x 2 3x 2

061 A 2014 0 7 104 Trapizoatial 0 6 Rectangular

Match each piecewise function to its graph x x 0 f x x x 0 f x 2x 1 x 1 f x x 3 x 0 4 x 2 5 x 3 f x x 3 x 3 3x 1 x 2 f x 1 x 1 x 2 DRAG DROP THE ANSWER

10 A piece of wire of length 178 cm is cut into two parts The first part is bent into a square and the second part is bent into an equilateral triangle If the length of a side of the square is 6 cm longer than that of the 6 marks equilateral triangle Find the lengths of the two parts of the wire cut out

Lorene plans to make several open topped boxes in which to carry plants The boxes are mac 5 in squares from each corner The length of the original piece of cardboard is 10 in more tha dimensions of the original piece of cardboard x 10 The dimensions of the original piece of cardboard are 5 in in by 5 in in

Let S p x E P p 1 p 2 a Show that S is a subspace of P b Find a basis and the dimension of S c Find the coordinates of the vector p x 5x 15x 7 relative to the basis found part b 0 Determine whether the following statement is true or false Justify your answer with a proof or a counterexample a The planes x y 2z 5 and x y z 1 2 3 1 1 2 s 3 0 7 t are perpendicular b If A is a matrix such that A is symmetric then A is symmetric c If u v w is a basis of a vector space V then u u v w u 2v 2w is also a basis of V

R If f x ax 4 and gkx x 3x a 2f 3g 1 7 then find the vala 1 9

One factor of the function fix x 9 20x 12 is x 6 Describe how to find the x intercepts and the yintercept of the graph of fox without using technology Show your work and include all intercepts in your answer

Is x 5 a factor of f x x 4x 3x 7 Explain your reasoning

8 There are some questions in a quiz 3 marks will be awarded for each correct answer and 2 marks will be deducted for each wrong or blank answer It is given that Karen answered all questions and she scored 40 marks in the quiz If Karen got 12 more correct answers than wrong answers find the total number of questions in the quiz 5 morka

Find 5 solutions to the equation y 3x 1 X 2 1 0 1 2 Y

Solve the compound inequality and give your answer in interval notation 3 10x 1 6 15x 21 AND 3x 1 3x 23

Solve the compound inequality and give your answer in interval notation 3x6 12 OR 3x 8 7

Solve and graph the compound inequality 1 x 1 5 Select the correct choice below and if necessary fill in the answer box to complete your choice O A The solution set in interval notation is O B There is no solution

Describe the shape of the data summarized in the histograms below 15 H P

35 x 2 2

5 The foot bottom of a ladder is placed 1 5 m from a wall The ladder makes a 70 angle with the level ground Find the length of the ladder le X 1 5 m at about 40 m from the