Quadratic equations Questions and Answers

2 To which number set s does the following number belong 17 Multiple answers may be correct Mark all correct answers real numbers rational numbers counting or natural numbers integers irrational numbers whole numbers

1 To which number set s does the following number belong 8 Multiple answers may be correct Mark all correct answers integers real numbers whole numbers rational numbers counting or natural numbers irrational numbers

Write the value of the discriminant of the following quation decide how many different real number roots the quation has and determine how many points the parabol will intersect with the x axis Do not solve the equation 3x 6x 2 0 discriminant is 60 indicating there are no real roots with the parabola not intersecting the x axis at all discriminant is 60 indicating only one real root with the parabola intersecting the x axis at only one point discriminant is 60 indicating there are two real roots with the parabola intersecting the x axis at two places

The distance that a free falling object falls is directly proportional to the square of the time it falls before it hits the ground If an object fell 83 ft in 4 seconds how far will it have fallen by the end of 9 seconds Round your answer to the nearest integer if necessary Answer 2 Points Keypad Keyboard Shortcuts

2 Factor the trinomial 2 52 14 O x 7 x 12 x 2 x 7 O x 4 x 2 O x 12 x 4

38 Multiply the following binomials 76 y 4b y O 286 4by y O 286 3by y O 28b 11by y O 286 7by y

Jamal rides his scooter to a skate park on a downhill trail from his home The trail is 12 miles long and his uphill speed on the way home is 4 miles per hour slower than his downhill speed If it takes him 4 hours longer to get home than it did to get to the skate park determine his downhill speed Enter your answer in miles per hour and rounded to one decimal place if needed

ynthia works at a factory where they make chairs the beginning of the day as Cynthia greets other orkers and gathers her materials she gets little done At d of the day as she gets fatigued and as she cleans up he ork station her production drops off The number of cha nthia makes each hour can be modeled by the equation 11t 1 375t where b is the number of chairs and t is e number of hours since she begins her shift aph this situation on your calculator or on a sheet of pa hat is a reasonable domain and a reasonable range for t D t 8 R b 22 D 0 t 8 R 0 b 22 D 0 b 22 R 0 t 8 nh 22 D

28 Choose whether the expression is a result of multiplying conjugates together squaring binomials both or neither 4x 25 O multiplying conjugates squaring binomials O neither

5 13 6 Use the quadratic formula letting a 1 b 5 and c 19 X x 5x 13 and y2 6 Find the points at which they intersect all of these are practical ways to solve the quadratic graphically Set the equation y x 5x 13 equal to 0 1 J 1 CAL O let y

X 14 8 6 9 6 04 8 6 9 6 4 Simplify the following expression x 7x 6 x 4x 3 O 2x 17x 3 O 7x 17x 18 10

25 For the following quadratic Find the value of the discriminant 2 7z 2 O 32 O 53 O 41 O 46

either the simplest fractional form or as an integer 86 15 296 0 1 2 01 10 00 3 3

1 Using a graph find all the roots of the quadratic x 4x 1 rounding to the nearest tenth 0 3 3 7 3 4 0 6 0

15 Simpliry the given expression 4xy 5x y O 20x y4 O4xy 52 g O 9x5y O 20x5y5 44 16 Simplify the following polynomial g h 3gh 7gh 3gh 8 O g h 6gh 7gh 8 O g h 7gh 8 O 6g h 8 6g h 8

17 Multiply by using the pattern you just learned 7x 7y 7x 7y 18 Solve the following by taking the square root 4t 44 t O 3 28 O 3 32 O 3 40 O 3 37

1 Factor the following trinomial a 4a 12 Factored trinomial 2 Using the discriminant state the number of solution for the following equation 2z 5 O one real root O two real roots O three real roots o real roots

13 Express y x 9 13 in standard form O y x 18x O y x 18x 94 O y x 8x 16 O y x 8x 16 14 Choose whether the expression is a result of multiply conjugates together squaring binomials or neither 36y 72y 27 O squaring binomials O multiplying conjugates O neither

mig using the quadratic formula x 2 318x 1 936 0 O 2 970 and 0 652 O 2 530 and 5 941 O 3 623 and 8 937 O 3 623 O 1 092 O This quadratic has no solution 2 Solve the following by taking the square root 4v 21 12 Round your answer to the nearest hundredth v

x 5 x 10 O x 50 x 5 x 50 x 5 O x 5 x 10 4 Solve the following by taking the square root t 40 t O 6 39 O 6 23 O 6 32 16 30

5 Multiply the following binomials a b a b O a 6 O a 2ab b O a 2ab b O a 6 6 Factor the following binomial 49a 9 O 7a 3 7a 3 O 49 a 3 a 3 O 7 a 3 a 3 O 7a 3 7a 3

find all the roots of the quadratic x x 6 y All changes saved

Refer to functions s and t Find the indicated function and write the domain in interval notation s x Part 0 2 Part 1 of 2 x 1 2 x 9 1 x x 3 1 x

What interval notation represents the data graphed below 2 1 0 1 2 3 4 5 OA 2 U 4 00 OB 2 U 4 OC 2 U 4 OD 2 U 4 00 Reset Selection

Identify the location and value of any relative maxima or minima of the function Ignore points on the boundary of the graph If there is more than one answer separate them with the and button

Given the functions f x 4x Evaluate the function 3 is 8 x x 7 x 5 3 for x 3 Write your answer as an integer or simplified fraction Select Undefined if applicat 8 Undefined h x

Claire needs to borrow 4000 to pay for NHL season tickets for her family She can borrow from a finance company at 2 77 add on interest for 4 years or she can borrow from a credit union 48 monthly payments 93 48 each Find the APR for each loan using a TVM solver and decide which one is Claire s better choice The APR for the finance company loan is 1 Type an integer or decimal rounded to the nearest hundredth as needed

a baseball is dropped from a stadium seat that is 77 feet above the ground its height s in feet after t seconds is given by s t 77 14 2

e safe load L of a wooden beam supported at both ends varies jointly as the width w and the square of the depth d and inversely as the length I A wooden beam in wide 9 in deep and 3 ft long holds up 29853 lb What load would a beam 2 in wide 3 in deep and 14 ft long of the same material support Round your nswer to the nearest integer if necessary Answer Keypad Keyboard Shortcuts

O 0 79 O 1 05 O 1 33 O 0 68 2 If 2 cups of flour are needed for 5 dozen tarts how many cups of flour are needed for 7 dozen O 2 cups O 4 2 3 cups O 14 cups

there are 16 purple shades in a large box of 48 crayons ercentage is there of crayons with purple shades Roun earest whole number 32 33 0 33 0 32

X 5 7 Hammer City finds 5 out of 340 hammers are flawed If they test 1438 hammers every week how many can they expect to be flawed Round up x 2 3 Solve 10 3 x 8 Round your answer to the nearest hundredth if necess

14 Solve for x 6 09 10 O 6 0 1 1 0 O 12 18 X 36 x 6

a Do the following problems without a calculator For each problem display the answer you get Then check on the calculator Display your answers 1a 12 5 4 x 3 2a 2 x 5 6 2 0 3a 1684 4a 16 8 4 5a 12 2 9 2 6a 8 2 2 1 7a 2 5 9 8a 2 x 5 2 9 9a 8 2 1 10a 3 11a 100 5 2 12a 100 5 2 b What steps did you use to get the answers c What do we learn from the calculator about Order of Operations d Why is it important to use Order of Operations e Insert parentheses if needed in each of the following expressions so the answer for all problems will be 45 1e 4 3x7 4 2e 2 5 2 3e 2 x 3 3x5 4e 3 1 10 9 3 3 6

2at 2 Given the formula F solve for a 3 5 Make sure to use appropriate parenthesis and notice which letters are capital letters and which are lowercase letter

15 Given the formula V Tr2h solve for h O OF F O 77

6 The formula p models the relationship between atmospheric pressure p in inches of mercury and altitude a in miles At w location does the model predict the pressure to be about 23 93 in of mercury Hint 1 mi 5280 ft 69 1 a 2 3 Sahara Desert average alt 1500 ft Kalahari Desert average alt 3100 ft

please answer the question exactly as it is posted filling the table in DO NOT answer this question if youre not going to fully complete it 3 Solve the following inequality and graph the solution set on a Real Number Line Be sure to show your boundary point s number line and test value work Express the solution set in interval notation x 7x 9x 63 0 Interval Test Value Work Solution

9bh 2 Given the formula M solve for b 7 Make sure to use appropriate parenthesis and notice which letters are capital letters and which are lowercase letters b

3 Given the formula A solve for u Ou U Ou 4 Ou 3 74 Ou U

3 Solve the inequality set Graph the solution on a numberline x 10 8 O2 18 O2 r 18 O2 x and x 18 O2 x and x 18 O all real numbers no solution

4 Solve the inequality set Graph the solution on a numberline 11 6 or 2 4 13 Ox 9 Or 5 Or 9 or 5 Or 9 or 1 5 O all real numbers no solution

2 Solve the inequality set Graph the solution on a numberline 7 14 or 5 13 Ox 8 O 8 or 7 O 8 or x 7 0 7 O all real numbers no solution

4 Analyze the following graph of a system of two equations Determine the x and y values of the solution of the system y x

Analyze the following graph of a sy Determine the r and y values of the solution of the system State your answers as decimals not fractions X

1 Analyze the following graph of a system of two equations Identify the coordinates of the solutions to the system More than one answer may be correct check all that apply 0 0 3 0 0 3

n Determine the r and y values of the solution of the system y

10 Simplify completely 252g h O 6g h5 7gh O 6g h 0 7gh O 6gh 7g h5 O 6gh 7g h 0 10 11 If n 36 n 3 12 Simplify 10 5

Sun piy Tom x 8 Solve for b Do not use a calculator Keep radical i 6 112 b 9 Simplify completely 252c d7 O 6c d 7d 6c d 7d

2 Simplify h 6 h 7 3 Simplify completely 48g h6 O 4g h 3 O 3gh 4g h5 O 4g h5 3