Quadratic equations Questions and Answers

Which of the following is equivalent to 18 25 18 5i 5i

What are the solutions to the inequality x 3 x 5 0 x 5 x 3 x1 3 x 5 x 5 x 3 O

Which equation is y 6x 12x 10 rewritten in vertex form Hint graph both to see which one matches the graph y 6 x 1 4 y 6 x 1 16 y 6 x 1 10

Which inequality in vertex form presents the region less than or equal to the quadratic function y 1 z 1 3 Oy 2 1 3 Oy 2 1 3

Which value must be added to the expression x 16x to make it a perfect square trinomial Completing the Square what is the new c term 256 64

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

A projectile is launched straight up from the ground with an initial velocity of 120 ft s If acceleration due to gravity is 16 ft s after about how many seconds will the object reach a height of 200 ft Graph the equation and find the x value where y is 200 h t 1612 120t

Question Determine the domain on which the following function is decreasing 1 10 98 10 S 6 4 8 9 10

Which equation shows the quadratic formula used correctly to solve 7x2 9 x for x 1 1 4 7 9 2 7 X 1 1 4 7 9 2 7 1 1 4 7 9 2 7

What is the square root of 16 8i Ai

Solving Quadratics Solve each equation by factoring 11 24r 140 0 A 16 C 10 6 5 3 x 11x 13 13 A 18 16 C 11 0 5 n 14n A 14 0 C 1 8 B 10 14 D 4 1 7 m 121 0 A 3 2 C 13 0 B 15 5 D 20 0 B 10 0 D 1 7 B 17 7 D 11 11 9 m 6m 2m 128 A 3 0 C 3 5 B 16 8 D 16 7 4 22 x 9x 10 0 A 14 1 C 10 1 6 8 10 4 b 16b 17 2 A 7 5 C 15 6 6 p 29 p 180 A 9 0 C 16 15 10 4n 4n B 1 4 D 10 11 A 7 12 C 8 12 8 9x 2x 95 16x 10x A 14 4 C 9 18 B 8 15 D 1 15 B 9 20 D 9 6 B 19 0 D 19 5 102 6 3n B 12 4 D 1 11

7 15 102 15 100 15 2 1500 30 1530 Yukar da verilen 15 102 i leminde bo b rak lan yere a a dakilerden hangisi ya z lmal d r A 15 100 2 C 15 100 2 B 15 30 2 D 15 30 2

6 0 cosx 1 2sin2x

27 Show that the equation 15x c 0 has at most one root in the inter 2 2 28 Show that the equation x 4x c 0 has at most two real roots

procal Function Notes Reciprocal Function f x Ex 1 Graph f x 2 1 0 1 Y 2

The function y f x is graphed below What is the average rate of change of the function f x on the interval 6 x 2 20 16 12 00 12 9 20 6 8 10

2 Graph f x 3x X Y Name the asymptotes Domain Range

3 Fill in the table shown for y value x V 1 2 Substitute the given value into the equation to find the missing 3 4 5 6 0 5

1 25 5 2 12 75 3 8 50 5 5 10 6 4 25 1

In an inverse variation x 6 y a What is the equation that represents the inverse variation b What is the value of y when x 15 b a

Work Required Consider the following system of equations 2 g 3z 3 2z z 0 2y 7z 6 Solve the system and provide a geometric description of the solution set in R There is no solution A point Aline Aplane

x y 2 6 2 6 4 12

The movement of the progress bar may be uneven because questions can be worth more or less including zero e Which function is represented by the graph below Of x 0 5x Of x e 0 5x Of x log 0 5x Of x ln 0 5x

3 Use the properties of equality to solve the equation 3x 2 x 11x 9 State which property justifies your first step and why you chose it Check your solution

1 Guess a number for x that would make the equation true Check your solution 5x 2 8 2 Use the properties of equality to solve the equation 7x 4 x 12 State which property justifies your first step and why you chose it Check your solution

3 Complete the following chart usilly these may not exactly match your periodic table 2 marks Mass Number 63 55 9moto qui pt to 29 Atomic Number Protons Symbol C4 m 29 Neutrons Electrons 29101327 Charge 2 2 X

Using the graph below complete the transformations h x x 1 2 1 The graph is 2 The vertex is horizontally shifted 3 The vertex is vertically shifted than the parent function 4 The vertex is located at units to the units

Show What You which graph is red by the function 2 3 2 2y 2 6 V SH 12 31 12 2 14

check your answer x x 3 2x Type a response 1

2x x 3 0

check your answer 3x 4 4x 3 Tyne a response

check your answer 4x 2 x 1

9 2n 10n 132 0 11 a 10a 21 0 13 6m 42 4m 15 x 15 5x formula 10 3x 5 0 12 4v 2v 2 14 6v 22 16 6r 30 3r

Factor each completely 1 8 x 5x 16x 10 1x 8x 5x 8x 5x 1x 2 x Sx 3 x 15x x 3 51 36342167 56 38 7 21a 49a 9a 21 9 7 8r 28r 32 12 30v 12v 25v 10 60 su 20 S Su 2 60 SXsu 2 4 28x 12x 47x 3 4x 7x 3 1 7x 3 4x 7x 3 6 fox 35x 48x 42 8 2k BY 2 8 16K 7k 56 10 49x 35x 21x 15

3 6 Using Quadratic Formula and Discriminant Homework AIC Find the discriminant of each quadratic equation then state the number and types of solutie 1 4x 8x 4 0 2 7x 5x 10 0 3 6x 7x 5 0 5 5n 6 8n 7 2x X 4 3m 6m 3 0 6 9p 1 6p PERK 8 4r 8r 6

NAME Factor each completely 21 5r x 6 23 3x 5x 12 25 66 29b 9 27 3b 8b 4 29 10x 23x 6 22 7x 19x 6 2x 21x12x 6 7x 1x 3 2x 2 24 10x 9x 9 G 10 67 157 2x 5x 3 Ext 26 9k 62k 7 dk 126 4klk 14 L 28 2x 7x 9 2x2 0 x 2x 30 4n 11n Cynz g 4 NCC

Review Factoring 1 Notes Homework SSE Factor the common factor out of each expression 1 7p 3p 6p 9p 3 18 18x 81x 18x 5 21x 14x Factor each completely 7 k 12k 35 9 x 7x 6 11 5x 35x 30 2 40x 50 45x 15x 5 8x 10 39 4 15m 10m SM 3M 2 6 9n 81n 9n 45n 41 4 1 9n 1 sps 8 n 3n 28 10 x 15x 50 15 x x 10 12 2x 20x 18 2 x x 4 2 x 4 x 1

Name Algebra 1 Review Factoring GCF a 1 GCF then a 1 Factor the common factor out of each expression 1 90x 63x 3 7k 21k 5 2v 14v Factor each completely 7 n 11n 30 9 v 10v 9 2 81x6 90x4 36x 63x 4 100v5 40v 80v 90v 6 24n5 30n 24n 6n 8 x x 72 10 r 90

Determine the open intervals on which the function is increasing decreasing or constant Enter your answers using interv notation If an answer does not exist enter DNE f x x 2x Encreasing decreasing constant 2 1 y 6 6 2 1 2 3 4 X

Divide x 8xy 20 x 8xy 15y Simplify your answer as much as possible 0 2 x 2y 4x 20y 5 X

92 Cost of Driving The cost of driving a car includes both fixed costs and mileage costs Assume that insurance and car payments cost 350 per month and gasoline oil and routine maintenance cost 0 29 per mile a Find a linear function f that gives the annual cost of driving this car x miles b What does the y intercept on the graph of f represent

Question Click and drag like terms onto each other to simplify fully 6y 2x 2x 7y 6x 2y 7 7 6y 4x 7y 6x 2y

Write the reduced radical form of the following expression 6 6 2 a 6 b

1 The parent function for each function below is y x Graph each function below on a separate piece of paper take a picture and upload Do not use a graphing utility use transformations a y x 2 b y x 1 c y 3 x 1 4

In many classes a passing test grade is 70 Using the formula A 10 R what raw score R would a student need to get a passing grade after her score is adjusted The student would need a raw score of Check The voltage V of an audio system s speaker can be represented by V 4 P where P is the power in watts of the speaker An engineer wants to design a speaker with 400 watts of power What will the voltage be The voltage would be volts

Please show ALL necessary work or no credit will be given 1 Find the inverse of the relation 1 0 2 1 3 0 4 2 2 Show steps to find the inverse of the function Is the inverse a function Give a reason for your answe a f x 3x 1 H h g x 1 2 x 5

Simplify the radical expression X20 32 Select one O a x y O b x y O c x 6 28 O d x y

The index is Check Va When there is more than one real root an n is even the nonnegative root is called the

Find all the real cube roots of 64 Write none if there are no real roots Answer Check Find all the real cube roots of 27 216 Write none if there are no real roots Answer Check

3 3 3 3 3 3 Answer Check Write in radical form x 5 Select one a O b O c O d x 5 x 5 x 1 x