# Algebra Questions

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Algebra

Complex numbersThe table of data lists input output values for a function Complete parts a through c a Is the change in the inputs x the same Select the correct choice below and if necessary fill in the answer box to complete your choice OA Yes and it is equal to OB No X 11 28 96 113

Algebra

Quadratic equationsFind all real solutions of the equation by factoring Enter your answers as a comma separated list 4x 4x3 0 X

Algebra

Matrices & DeterminantsYou may need to use the appropriate technology to answer this question Develop the analysis of variance computations for the following completely randomized design At a 0 05 is there a significant difference between the treatment means A 136 119 113 107 130 114 130 95 xj 2 s 186 29 118 Treatment B 108 113 125 104 106 110 98 113 105 88 107 C 91 82 86 101 88 116 111 119 99 97 99 95 78 164 89

Algebra

Quadratic equationsThe function g is related to one of the parent functions described in an earlier section g x x 6 a Identify the parent function f f x b Describe the sequence of transformations from f to g Select all that apply O reflection in the x axis horizontal shift of 6 units left Overtical shift of 6 units upward Overtical shrink Ohorizontal shift of 6 units right c Sketch the graph of g O y y 5 10 5 4 2 2 4 V V 5 15 10 5 10 5 4 2 15 y 15 10 5 5 2 d Use function notation to write g in terms of f g x f 4 X X 15 10 10 M y 10 5 5 10

Algebra

Quadratic equationsSolve the following system of equations graphically on the set of axes below 1 2 5 y 10 9 8 7 6 5 y x 4 Plot two lines by clicking the graph Click a line to delete it 3 2 1 7 1 N 2 co 759 2 10 7 5 1 2 9 10 x

Algebra

Quadratic equationsadditional parentheses 000000 1 5x 3 2 2 5x3 4 25 2 15 2 2x2x2 3 3 x 5 13 441 25420H 3 4 3 x 4 3 25 4 3 X 6 2x2 5 4 5 10 2 2 1 5 6 1 3 2 6 x 2 5 2 8 X7 56 8 3 2 2 17 7 5 1 5 5

Algebra

Quadratic equationsUse Gauss Jordan row reduction to solve the given system of equations system is dependent express your answer using the parameters x y ar x y z 8x y 32 0 8x y 2z 5

Algebra

Quadratic equationsMatch the graph with its function using the x intercepts 4 4 4 4 24 y x x 2 y x x 2 y x x 2 y x x 2

Algebra

Quadratic equationsA ball is projected upward from the ground Its distance in feet from the ground in t seconds is given by s t 16t 126t At what times will the ball be 223 feet from the ground

Algebra

Matrices & Determinantsnd the solution set of each linear system Identify inconsistent systems and dependent equation x 3y z 20 x 4y z 18 x 3y 4z 19

Algebra

Quadratic equationsA conical tank contains seawater to a height of 2 ft The tank measures 12 ft high and 5 ft in radius Find the work needed to pump all the water to a level 2 ft above the rim of the tank lb The specific weight of seawater is 64 ft3 Approximate the answer to three decimal figures

Algebra

Permutations and CombinationsConsider the following planes 5x y z 5 15x 3y 5z 25 e Find the engle in degrees between the two planes Round your answer to two decimal places 45 25 X b Find a set of parametric equations for the line of intersection of the planes Use t for the parameter Enter your answers as a comma separated list of equ x y 5 5z 5

Algebra

Quadratic equationsOne leg of a right triangle is 2 millimeters longer than the shorter leg and the hypotenuse is 4 millimeters longer than the shorter leg Find the lengths of the sides of the triangle The length of the shorter leg is The length of the longer leg is The length of the hypotenuse is millimeters cubic millimeters square millimeters

Algebra

Quadratic equationsThe length of a rectangle is 19 centimeters less than five times its width Its area is 30 square centimeters Find the dimensions of the rectangle The width is and the length is

Algebra

Quadratic equationsThe product of two consecutive room numbers is 306 Find the room numbers The number of the first room or the smaller room number is x 1

Algebra

Quadratic equationsPart 4 Write a real world situation for each expression below be creative A b 12

Algebra

Sequences & SeriesBONUS Bonus will be graded as noted in the rubric with the understanding that a student s grade cannot exceed 105 points Part 6 Bento boxes b are special boxed lunches in Japanese cuisine Sushi rolls r are also a popular lunch item usually made of rice seaweed vegetables and either raw or cooked fish Steven wants to buy 3 bento boxes b and 2 sushi rolls r A Write an expression that represents Steven s purchase B Each bento box is 10 yens and sushi rolls are 8 yens How much did Steven spend on his purchase Show your work

Algebra

Complex numbersEvaluate each expression show your work A 2c 4 when c 3 B 3 t 8 when t 4 C 43 x 2 when x 5

Algebra

Complex numberse From the zeros of the numerator and denominator of R x divide the x axis into intervals Determine where the graph of R is Above or Below the x axis by choosing a number in each interval and evaluating R there In short fill out the chart below and do an Interval Analysis as done in class 12 points Interval Number Chosen Value of f Location of graph Point on graph R x x 8x 12 X 9

Algebra

Complex numbersWhat is the range of the function graphed below 3543 1 y 4 D 3 y 3 379199 44 5 B x

Algebra

Quadratic equationsThe function h defined by h t 49 4 9t 10 t models the height in meters of an object seconds after it is dropped from a helicopter b C Find or approximate the time when the object hits the ground Explain or show your reasoning From what height is the object dropped Explain or show your reasoning Where is the vertex of the graph

Algebra

Quadratic equations3 A quadratic function is defined by g x x 4 7 What is the vertex of the graph of function g C a b Does the vertex represent the minimum value or the maximum value of the function Explain or show how you know If you were to shift this graph 6 units down from where it is now what would be the equation represented by the new graph

Algebra

Quadratic equationsNAME T Introduction to Quadratic Functions Assessment 2 Here is the graph of a quadratic function f 1 2 a b C y 1 O 1 2 3 4 5 6 2 0 2 6 0 3 4 5 5 DATE 2 2 24 4 4 7 X Write the equation for f x in vertex form Write the equation for f x in factored form Write the equation for f x in standard form 2 A quadratic function is defined by p x x 1 x 3 Graph the function on the coordinate plane and label the coordinates of the x intercepts the y intercept and the vertex y 5 4 3 2 1 WN TO 6 5 4 3 2 10 1 2 3 T 2 3 4 PERIOD 5 X

Algebra

Quadratic equationstroduction to Quadratic Functions Assessment 2 Here is the graph of a quadratic function f y 1 2 1 a b C 1 2 3 4 5 2 0 2 3 4 6 0 5 en 4 4 16 7 X Write the equation for f x in vertex form Write the equation for f x in factored form Write the equation for f x in standard form

Algebra

Quadratic equations2 2 3 Select Select Two numbers multiply together to equal 90 but add together to equal 9 What are the two numbers Select 4 Select 5 6 and 1 7

Algebra

Quadratic equations2 2 Two numbers multiply together to equal 90 but Select add together 9 What are the two numbers Select t Select 2 Select and 1

Algebra

Quadratic equations6 2x 2 10 When you square both sides what is the resulting O equation in the next step before you solve for x O O 2x 2 100 2x 2 10 1 2x 2 100 2x 2 10 C

Algebra

Quadratic equationsb Where are the x intercepts d Where is the y intercept e Where is the vertex f Graph the function on the coordinate plane and label the coordinates of the x intercepts the y intercept and the vertex X

Algebra

Quadratic equationsWhat is the quotient of 3x4 4x2 8x 1 x 2 Watch for any missing terms 3x 6x 8x 24 47 x 2 3x 6x2 8x 24 47 3x 6x 8x 24 3x 4x 8x 1 47 3x 4x 8x 1 O3x 6x 8x 24 47 X 2

Algebra

Quadratic equationsJoshua decides to use synthetic division to find the quotient of 3x 8x 2x 3x 10 x 2 What value from the divisor should he write in front of the coefficients 00 3 S S

Algebra

Quadratic equationsWhat is the quotient of x3 3x2 5x 3 x 1 Ox 2x 3 Ox 2x 3 Ox 3x 8 x 2x 7 0 0 0 0

Algebra

Matrices & DeterminantsWe can find the remainder for the quotient using either substitution or synthetic division as discussed in class Using either method explain whether or not we can conclude that x 5 is a factor of the polynomial f x x 17 15 Show your work process to find the remainder Your answer must include what that remainder value is and if it indicates x 5 is a factor or not

Algebra

Quadratic equationsdentify the graph of the function g x f x 1 2 from the transformation of the parent quadratic function f x

Algebra

Quadratic equationsSolve using the square root property m 3 12 X D Font Size 4 A Q A BIUS X x 99

Algebra

Quadratic equationsIdentify the equation of a parabola with a minimum value of 1 of x x 2 3 Of x 2 x 2 3 o f x x 4x 5 of x x 4x 7

Algebra

Complex numbersMATCH the indicated operation on the left with each simplified expression along the top Each row should contain exactly one check mark 1 7i a 2 3i 3 4 b 2 3i 3 4i c 2 3i 3 4i 2 3i 3 4i d THE 6 i O 5 1 0 24 0 68i 18 000 0 1

Algebra

Quadratic equationsThe figure shows a graph of the function f x in the xy coordinate plane 5 10 5 5 C Use the dropdown menus to indicate whether each statement is true or false f x has A a minimum of 8 B two real zeroes C a decreasing interval from 1 D a y intercept of 7 E A vertex at 1 8 F f x 0 over 0 5 Sign out

Algebra

Quadratic equationsSolve the equation by completing the square x 8x 20 Ox 8 72 O x 10 2 O x 20 4 Ox 4 72

Algebra

Sequences & SeriesA ball is thrown into the air with an upward velocity of 40 feet second Its height h after t seconds is given by the function h t 16t 40t 12 Answer the following questions by typing your answer in the box provided for each part A In how many seconds does the ball reach its maximum height Round your answer to two decimal places B What is the maximum height of the ball Round your answer to the nearest foot feet seconds

Algebra

Quadratic equationsWhich of the following is true about the solutions for the equation 3x 5x 4 0 O Information about the solutions cannot be determined O There is only one real solution O There are two real solutions O There are two non real complex solutions

Algebra

Quadratic equationsSolve the equation by using the quadratic formula 2x 8 x 1 i 65 2 0 x X 0 x 0 x 1 65 4 1 65 65 4 1 63 4

Algebra

Quadratic equationsCompared to the quadratic parent function the graph of g x and translated from the parent function 1 2x 6 is

Algebra

Sequences & SeriesThe height h t in feet of the ball above the ground t seconds after being thrown can be modeled by the function h t 16t 40t 5 What is the meaning of the number 5 the function h t The ball takes five seconds to reach the ground The ball reaches a maximum height of five feet O The ball takes five seconds to reach its maximum height O The ball was thrown from an initial height of five feet d Fab 2 9 29 US

Algebra

Quadratic equationsWhen asked to write f x 2x 16x 7 in vertex form Carlos showed his work by writing the following Step 1 f x 2 x 8x 7 Step 2 f x 2 x 8x 16 7 16 Step 3 f x 2 x 4 9 Is Carlos correct in his reasoning Explain your reasoning B I US X X