Quadratic equations Questions and Answers

Graph the following function At each step sketch a graph noting the change from the previous version f x 3 x 2 4 Begin with the SKETCH of the basic function in f x x Use the axes below to show a step by step transformation of the basic function Please note the change from the previous version briefly in words f x x 2 f x 3 x 2 f x 3 x 2 f x 3 x 2 4

2 Find the next two terms in the geometric sequence 3 4 28 7 1 1 21 189 O 9858 16 64 63 098 5600 16 16 64 O 19 63 189 O 1 O 16 63 189 64 256 567 567 256 64 256 189 567 None of these are correct

f x 3 x 2 4 Begin with the SKETCH of the basic function in f x x

Use the axes below to show a step by step transformation the basic function Please note the change from the previou version briefly in words f x x 2

6 Find the sum of the geometric series a 108 az 12 r r S3 co 1

sider the following graph of g x Write a formula for g x that describes the transformations performed on the basic fur Answer STO g x IE 10 30 5 Enable Zoom Pan

37 of the 192 az 3 r a1 O 108 129 O 142 136 O None of these are correct a1 CHE 1 2 2 What is Sn of the geometric series with 32 r 5 and n 5 O 877 O 878 O 902 898 series

10 2 2 2 4 Find the sum of the geometric series 9 5 Find the sum of the geometric series 4 6 128 r 128 r 2 S6 x x 6 Find the sum of the geometric series a 108 a3 12 r 3

tic 6 4 k 1 1388 1365 O 1395 O 1371 O None of these are correct 8 Find S5 of the sum of the geometric series 1 1 729 a5 9 r 555 532 O 523 535

13 Find the sum of the geometric series 10 3 k 1 SA 14 Find the sum of the geometric series 9 a 243 r 3 x

4 Find the next three terms in the geometric sequence 5 1 1 125 x x

12 Calculate the ag term of the geometric sequence with Az 64 and r 4 O 1 65536 O 262144 O 1 262144 O None of these are correct O 65536 13 Find the next term in the geometric sequence 10 21 1 15 7 135 56 56 135 28 45 45 28

9 For the geometric sequence find the two missing terms between and 81 5 11 12 1 81 13

Find the next three terms in the geometric sequence 5 1 Find a10 if a3 and r 2 a10 For the geometric sequence find the two missing terms 1 x x 27 Find the next three terms in the geometric sequence

4 Find the sum of the arithmetic series if a 27 a22 90 and n O S22 1281 S22 O S22 1298 O S22 17 1287 1283 None of these are correct 5 Find the sum of the arithmetic series if a 19 n 17 and d 4 22 6 Find the sum of the arithmetic series 21 16 21

13 Find the sum of the arithmetic series 41 47 53 59 65 71 77 83 89 95 10

9 Name the first five terms of the arithmetic sequence a 29 d 7 first term second term third term fourth term fifth term

3 In the summer time your friend wants to have a snow cone stand at a local grocery store parking lot You want to make sure he actually makes money The grocery store charges 300 per month All products are calculated to be 25 cents per customer Your plans are to sell each cone for 1 25 a Write a mathematical expression representing the cost of operation for a month b Write a mathematical expression representing sales c Create an equation that will represent overall profit of the operation for a month d Simplify the equation into slope intercept form and standard form What is the slope and explain its meaning in the context of selling snow cones What is the intercept and what is its meaning e Describe the method of graphing the slope intercept form and also the standard form of the equation f What is the domain and range of the equation Is the relation a function why g How many snow cones do you need to sell to break even in the first month h How much is the profit if you sell 425 550 or 700 snow

2 12 6 X a If you had to guess the equation for this quadratic what would your guess be b Explain why you think your equation matches the graph c Arrange your quadratic in standard form ax bx c what is the discriminant of your equation d Solve your equation using the quadratic formula Show your work

4 Thomas and Jenny went to a bakery to pick up some cookies for dessert Thomas bought 3 pumpkin cookies and 2 raisin cookies Jenny bought 2 pumpkin cookies and 4 raisin cookies Thomas consumed 870 calories and Jenny consumed 750 calories a Write a system of equations to represent this situation b Solve each equation for y and graph to find the solution How many calories are the pumpkin and raisin cookies c Solve the same equations using substitution and the elimination methods Compare all of your answers

functions interact with their factors zeros and graphs expl how to do the following a Find the zeros of this function p Use these zeros to write a factored polynomial in this Format x a x b c Multiply the factors together to create a polynomial Grap your polynomial using a graphing app or calculator Does y graph match graph the image above d Explain how you know your factors your polynomial the graph above and your graph all describe the same function fooplot com is my favorite graphing app online

Write a rational expression with at least one in the denominator and then analyze it using the following questions a Set your expression equal to 0 Does this expression have any solutions Why or why not b Set your expression equal to y and graph the equation on a graphing utility or on your calculator Are there any values that cannot be Explain c How do the numbers and variables in your equation relate to the features of the graph d Identify the denominator of your expression add 6 to the denominator only How does the graph change

1 Graph the following three equations on your own device and answer the questions below 1 f x 5x 7 2 f x x 6 3 f x 2 3 a What is f 10 b What is f 100 c What is f 1000 d Which function has the highest value at each value of e Use your answers to decide which type of function will increase the fastest f At what point did this function exceed the other two g Do you think this would work for any function of this type Why h If these 3 equations represent the growth of mucus in a membrane describe and state the domain and range for each function

2 Jack has 210 that he wants to spend on movies and games Each movie costs 20 and each game costs 15 If Jack wants to purchase at least three games what is th maximum number of movies he can buy Disregard tax movies Can he buy one more game with the change Yes or No

x 2y 4 More than one answer may be correct select all correct answers The two equations represent two lines that intersect at two points The two equations represent two lines that are parallel There is one x y solution for this system of equations There are infinite amount of x y solutions for this system of equations The two equations represent two lines that are the same line There are two x y solutions for this system of equations There is no x y solution for this system of equations

1 Your classmate Mark is struggling with a math problem from class and asks for your opinion He shows you an expression that he s trying to evaluate Mark s problem says to evaluate 3 x 4y if x 3 and y 1 What is the answer and how would you tell Mark to evaluate the problem Write your answer as an exact answer without any exponents Justify your answer orro Ou

2 Your friend Margret needs your help in solving a math problem that she got from her math teacher This was the problem x6 x x What number can be put where the question mark is Justify your answer

1 Travis decided to make a frame for his girlfriend s birthday The frame will be cut out of a piece of steel and the final area of the frame should be 30 in The inside of the frame has to be 11 in by 6 in The area of the piece of steel before cutting out the frame is Area 11 2x 6 2x in 11 in X 6 in What width should be Hint round to the nearest tenth in X

the grap of f is translated a whole number of units horizontally and vertically to obtain the graph of h The function f is defined by f x x 2 what is the expression for h x

Determine if the given equation is a proportion 5 5 11 6 1 13 11 1 11 13 5 13

6 Write the linear equation in standard form 2y x 5 x 7 On a separate sheet of paper graph the equation 2x 2y 4 8 Write the linear equation in standard form 3x 2 x x 9 Identify what a b and c would equal in standard fo Do not simplify the equation

3 Write the linear equation 4x 3y 12 in slope inte O y x 4 O y x 4 Oy x 4 O y x 4 4 Write the linear equation x 27 7y in standard form x 5 Write the linear equation in standard form

1 Write the linear equation in standard form 6x 19y

2 Solve 2x x 3x 10 0x 0 Ox 0 5 2 O 0 5 2

All changes 1 Travis decided to make a frame for his girlfriend s birthday The frame will be cut out of a piece of steel and the final area of the frame should be 30 in The ins the frame has to be 11 in by 6 in The area of the piece of steel before cutting out the frame is Area 11 2x 6 2x in 11 in 6 in What width should be Hint round to the nearest tenth X

7 Simplify the common factors out of the following expression 21a 18a 12a answer

15 Write the linear equation x y in standard form 5x 2y 2 5x 2y 2 5x 2y 2 5x 2y 2

5 In your physical education class you have to compete in a walk race Data from your race is in the scatterplot below Using the line fitted in the graph find the slope y intercept and the equation for the line that will model this data Make a prediction about how many feet will be traveled after 45 seconds

4 Linear relations are not functions when they appear graphically as linear relations are always functions horizontal lines O vertical lines

20 Solve the polynomial by factoring Identify the zeros roots of the equation More than one answer may be correct 7 39t 18 0 1 0 0 1 0 6 0 3 01 1 There are no real roots

f x 5x 1 x 7 Round your answer to the nearest hundredth if necessa 2 6 O 1 67 0 56 O 3 O Undefined 7 Tell which quadrant the point 7 10 will be in O Quadrant I Quadrant III Quadrant IV O Quadrant II

19 The length of a rectangle is 4 inches less than its width Write an equation for the area of the rectangle in terms of width w The total area is 145 Olxw 145 square inches O w 4 w 145 square inches O 1 1 4 145 square inches Ow 4 145 square inches

6 Given a right triangle AABC and C as the right angle if a 9 and b 5 c

5 If c represents the hypotenuse of a right triangle solve for the unknown side length a b 62 c 99 Round your answer to the nearest hundredth

3 Using the Pythagorean Theorem if in a right triangle leg b 11 and the hypotenuse c 20 what does the other leg a equal Round your answer to the nearest hundredth a

Question content area top Part 1 a Find the slant asymptote of the graph of the rational function b Follow the seven step strategy and use the slant asymptote to graph the rational function f x x 2 3x 28 x 7

6 Find a number halfway between and 1 4 16 x

2 70 292 972 30 52 Q 292 970 30 133 33

14 Express the following decimal as a fraction 0 6666

15 If x is an integer in the set of real numbers as x increases what happens to the expression