Quadratic equations Questions and Answers

3 L y 3 3 3

19 X 5 y 3x 3 6 54 3 2 LLC A 11 I 6 y x 3 6543

A Igebra 1 2 9 6 y x 3

3 y x 3 54 3 2 1 I 4 y

4 y 2x 4

HW 1 7 due Tuesday 1 8 N 02019 Kuta Software L L C All rights reserve Graph the equations shown below clearly labe 1 y 3x 4 2 y 5 5 1 3 2 1 N 6 x I 6 5

Name Oyinkansola Alaran rights reserved w clearly labeling at least two points 2 y 3x 1 6 5 4 3 2 1 2 Aft

13 14 15 13 23 42 A B 9 D 6 3 2 20 5 16 3 3 2 16 4 10 3 71 Write each expression in radical form 14 68 w 6 Write each expression in exponential form 15 A 7m C 24 B 68 D 36 Simplify B 7 D 2m

A C 2x Write each expression in radical form 5 106 3 A 26 C 106 Simplify B 7x D 10x 6 6 81x A 729x C x B 10b D 106 B 7776x D 729x LLC All

1 3 4 Algebra Prep C2024 Kuta Software LLC All rights reserve PRACTICE TEST Simplify 1 64u y6 A 2u 2u v C 2v 2u v 3 x 7 2 2 A 4x 1 9 B 2uv 3u D 2u 3u v B 216x D 1 3125x Write each expression in exponential form 4 10x A 2 C 2x 6 2 B 7x D 10x 2 2 343x A x C 240

Which equation has a graph that is a parabola with a vertex at 5 3 y x 3 5 y x 5 3 Oy x 5 3 O y x 3 5

Which phrase best describes the translation from the graph y 6x2 to the graph of y 6 x 1 6 unit left 1 unit right 1 unit left 6 unit right

Which phrase best describes the translation from the graph y 2 x 15 2 3 to the graph of y 2 x 11 2 3 4 units to the right 8 units to the left 4 units to the left 8 units to the right

Which equation is y 3x 12x 2 rewritten in vertex for O y 3 x 2 14 y 3 x 2 10 y 3 x 2 10 y 3 x 2 2

Write the first 6 terms of each pattern Start at 10 each time a Multiply by 2 then subtract 5 each time b Multiply by 5 then subtract 2 each time c Subtract 5 then multiply by 2 each time d Subtract 2 then multiply by 5 each time

Solve each system by elimination 1 x 5y 5z 2 4x 5y 4z 19 x 5y z 20 3 x 5y z 17 5x 5y 5z 5 2x 5y 3z 10 5 4r4s 4t 4 4r s 2t 5 3r3s 4t 16 7 x y 2z 6 3x 2y 25 4x y z 12 2 4x 5y z 18 2x 5y 2z 12 2x 5y 2z 4 4 4x 4y z 24 2x 4y z 0 5x 4y 5z 12 6 x 6y 4z 12 x y 4z 12 2x 2y 5z 15 8 5a 5b 5c 20 4a 3b 3c 6 4a 3b 3c 9

8 9 1 7 4p A p C p Solve each equation Remember to check for extraneous solutions ANSWER SHOULD BE AN INTEGEROR A FRACTION 8 NO POINTS IF YOU ANSWER AS A DECIMAL 1 3n Simplify 9 63r A 93 C 3 210 Z C 1 6n 2 B 4p D 6p 3 n 4 2 n 30r B D B 3r 210 D 1890 10 12 10 15p 4 10 8 A 54p p 36p 2p B 20 6p 8 15p C 70 9 D 14p 3p 9 2p 12 4 3 5 4 4 3 5 A 2 8 3 2 5 43 B 8 4 2 4 3 20 D

Simplify 11 64u v 3 3 2 2 A 4x 4 A 2u 2u v C 2v 2u v 5 A x 1 C 2x 6 Write each expression in exponential form 4 10x 5 106 A 26 C 106 B 2uv 3u D 2u 3u v Simplify B 216x 1 D 3125x Write each expression in radical form 3 6 6 81x A 729x C x B 7x 7 D 10x 6 B 10b D 106 2 B 7776x D 729x 4 2 343x A x4 C 2401x 2 B 256x 2 D 7x

6 13 2 3 2 A B D 6 3 2 2 20 5 16 3 77 3 2 10 4 4 10 3 71 Write each expression in radical form 3 14 6b A 6b C 6b Write each expression in exponential form 15 7n A 7n C 2n Simplify B 6b D b 16 64m A 100m C 1024m 5 B 7n 5 D 2n 4 B 8m D 10000m4

Using the graph of f shown find three intervals on which f is one to one making each interval as arge as possible Ay 6 3 3 6 The intervals on which f is one to one are Simplify your answers Use a comma to separate answers as needed Type yo answers in interval notation

9 Which point is on the line 6y 3x 0 A 2 1 B 2 1 C 1 2 D 1 2 Bizi sedy Hind

4n 8n 8n 4n

Exercises 49 64 Complete the following a Find f x for the indicated values of x if possible b Find the domain of f Use words or inequalities to describe the domain 49 f x x for x 2 5 50 f x 2x 1 for x 8 1 51 f x x 3x for x 3 2 52 f x 5 x 2x for x 1 53 f x 12 3x for x 1 4

Which expression represents the area of the rectangle shown a 4x 5 units b 4x 5 units c 3x 7x 4 units d 3x 9x 4 units 3x 4 x 1

What is the most completely factored form of the expression 45x 40x a 40 5x x b 5 9x 8x c 5x 9x 8 d 5x 9 8x

Exercises 43 48 A function g is defined a Write g as a set of ordered pairs b Give the domain and range of g 43 g 1 0 g 2 2 g 5 7 44 g 2 5 g 3 9 g 4 4 45 g 1 8 g 2 8 g 3 8 46 g 5 0 g 0 5 g 5 0 47 g 1 2 g 0 4 g 1 3 g 2 2 48 g 4 5 g 0 5 g 4 5 g 8 0

Exercises 27 42 Graph y f x by hand by first plotting points to determine the shape of the graph 27 f x 3 28 f x 2 29 f x 2x 30 f x x 1 31 f x 4 x 32 f x 3 2x 33 f x x 2 34 f x 2 2x 35 f x x 1

the value s of x when f x 4 There may be more than one response 1 point Distance away from car Feet 0 2 4 6 8 10 12 14 16 10 2 A B C 10 12 14 16 Time seconds D 18 E 20 22 LL 24 26

14 2 1 0 2

The Venn diagram here shows the cardinality of each set Use this to find the cardinality of the given set A 6 m AL ROC 12 14 B 4

The Venn diagram here shows the cardinality of each set Use this to find the cardinality of the given set A 10 7 B

The Venn diagram here shows the cardinality of each set Use this to find the cardinality given set A 9 6 C 8 B 8

4 A graph of f x x 2 is shown a Evaluate f 1 f 2 f 3 2 0 2 y NO 2 H f x x 2 4 6 b Find the domain and range of f 00 8

Functions and Their Representations HW 3 11 13 17 35 41 45 53 61 68 73 75 95 97 100 101 105 113 115 121 126 131 133 137 page 44 Sec 1 3 I Relations A relation is a set of ordered pairs If we denote the ordered pairs by x y then the set of all x values is the DOMAIN and the set of all y values is the RANGE Example 1 A physics class measured the time y that it takes for an object to fall x feet as shown in the table The object was dropped twice from each height x feet y seconds 20 1 2 20 1 1 a Express the data as a relation S D 20 40 R 1 1 1 2 1 5 1 6 S 20 1 2 20 1 1 40 1 5 40 1 6 b Find the domain and range of S 40 1 5 Find the domain and range of this relation 40 1 6 Example 2 Complete the following for the relation S 1 2 5 5 3 3 0 7 5 4

Identify a function symbolically Example 5 Determine if y is a function of x a y x 2 b x2 y 25

2 Let a function f be represented symbolically by f a Evaluate f 3 f 1 and f a 3 b Find the domain of f 2 3 A function g is given by g x x 2x and its graph is shown 3 2 1 y 32 7 1 1 3 2 g x x2 2x 3 a Find the domain and the range of g b Use g x to evaluate g 0 g 2 g 3 x 1 X

A function is a relation in which each element of the domain corresponds to exactly one element in the range The ordered pairs for a function can be either finite or infinite Diagrammatic Representation of Functions Example 3 Domain 10 D 15 20 Write f as a set of ordered pair f 5 1 Domain Range 2 f D R 2 3 4 R 3 5

1 How many planned to only grade papers 2 How many planned to grade papers or do household chores 3 How many did not plan to do any of these activities 4 How many planned to do at least two of these activities 5 How many planned to attend a football game and do household chores but did not have any plans to grade 6 How many planned to attend a football game or grade papers but did not plan to de household chores 7 How many planned to do at most one of these activities

A skydiver jumps from an airplane at an altitude of 2 500 ft He falls under the force of gravity until he opens his parachute at an altitude of 1 000 ft Using the initial velocity of zero approximately how long does the jumper fall before he opens his chute For this quadratic model we will let the y axis be the axis of symmetry h t 16t2 vt ho 9 7 s 2 4s 12 5 s 14 8 s

A softball pitcher throws a softball to a catcher behind home plate The softball is 3 feet above the ground when it leaves the pitcher s hand at a velocity of 50 feet per second If the softball s acceleration is 16 ft s which quadratic equation models the situation correctly h t at vt ho 3 50t 16t ho h t 16t2 50t 3 h t 5012 16t 3 3 1612 50t ho

1 A straight waterslide is 175 feet above ground and is 200 feet long What is the angle of depression to the bottom of the slide oldiroq

gles A 53 112 90 CS 36 978 9 to the est tenth 2 findside tan 6 ho B 12 5 B 38 C J A C Sin 38 of C 12 5 T CYSin 38 12 5 12 50 a 12 5 b Siss

3 5 O search 3 81 A 2 3x C 2x 3x 5 54m A 3m 2m C 3 3m II B 3 3x D 2 3x B 3 2 D 2m 3m 4 6 4 27a A 3 3a C 3 2a 6 81n A 3nN2n C 3 3 B 2V2 D 2 3 B 2n D 3

12 B 2 7 C 72 19 A

B 3 2m D 2m 3m B 2v 3uv D 2 2uv 4 B 3 2x y D 3y 3xy 6 8 6 81n A 3n 2n C 3n 3 8 64a7b A 2a 3ab4 C 2ab 3b 1010 24x y A 3xy 2x C 3 2x y B 2n 3 D 3 3n B 2a2a b D 2b 2a B 2x 3y D 2x 3x y

5 5 54m4 A 3m2m C 3 3m 7 24ux4 A 2u 3uv C 3uv 2 9 32x y4 A 2 3x y C 2y 2x B 3 2m D 2m 3m B 2v 3uv D 2 2uv B 3 2x y D 3y 3xy

e base of a 8 John wants to measure the height of a tree He walks in the cliff exactly 100 feet from the base of the tree and looks up The angle from the ground to the top of the tree is 33 How tall is the tree

Iding 30 by 6 You are standing 50 meters from a hot air balloon that is preparing to take off The angle of elevation to the top of the balloon is 28 Find the height of the balloon

In a loan database there are 14 loans to clients with 20 years of business experience Also there are 72 loans made to clients with a High School education In the database there are 82 loans to clients with 20 years of experience or who have a High School education How many loans were made to clients with a High School education who also had 20 years of experience

In a survey of 149 pet owners 57 said they own a dog and 66 said they own a cat 23 said they own both a dog and a cat How many owned neither a cat nor a dog