Quadratic equations Questions and Answers

The 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

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

Which 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

Solve 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

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

When 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

Question 1 10 Determine the discriminant of the function g x 2x 10x 5 O 10 60 100 O 140

Identify the quadratic equation that has solutions of 3 O y 3x 10x 8 y 2x 5x 12 Oy 3x 10x 8 y 2x 5x 12 and 4

11 12 x x 1 What is the extraneous solution to this problem Type a response

A quadratic equation is equal to 0 the constant is 24 the quadratic term s coefficient is 1 the linear term s coefficient is 2 What is are the solutions to the problem PICK TWO 6 2 1 4

3 x 6 2x 5 When you solve this problem what is the value of each side of the equation ROUND YOUR ANSWER IF NEEDED O O O 4 13 11 17

10 3x 7 x 3 3 2 4 3 1 4 C

5x2 x 8 When you square both sides what is the resulting equation in the next step before you solve for x O O O O 4x 28 5x2 x 8 5x 2 x 8 5x 2 x 8

Two numbers multiply together to equal 72 but add together 18 What are the two numbers Select Select Select Select and

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

Solve the following for x a 3x 11 2 b x5 2 2x 1 c 3x 1 2 x 3 2 marks 2 marks 2 marks

Find the quotient and remainder for x 4x 4x 10 x 3 5 marks

A school had a fund raising event The revenue came from three resources ticket sales auction sales and donations Ticket sales account for of the total revenue auction sales account for of the total revenue What fraction of the revenue came from donations of the revenue came from donations

Algebra X Slope intercept Form Find the slope of each line 1 3 SOR 2

Sketch the graph of each line 19 y x 4 21 y 4x 5 5 310 5 4 3 2 10 3 20 y 5x 1 2 10 22 y x 5 2 4 3 2 10

5 3 3 you fe 4 Algebra 13DC5 3 and 3 Name Slope intercept Form Worksheet Find the slope of each line 1 0 1 x 4 0 X 0 Y Y Y 3 1 XX 3 1 573 5 3 SOR 2 X X X2 X 3 33 4 4 3 2 1 3 3 0 ZI Elore 1 C1F 13 2 6 Name Eliya Love Date M 4 38 Us tercept form 3 1 2 Find the slon ato 2 1 2029 1 Period th X 1 1 x 3 X 1 X 3 X X 4 STOP 1 3 3 1 25 2 3 4 3 S

Find an expression for a cubic function f if f 4 160 and f 4 f 0 f 5 0 Step 1 A cubic function generally has the form f x ax bx2 cx d If we know that for some x value x p we have f p 0 then it must be true that x p is a factor of f x Since we are told that f 5 0 we know that x 5 is a factor Step 2 Similarly since f 4 0 then f x has the factor x 4 I to obtain a Step 3 Since f x has the factors x x 5 and x 4 then we must have f x a x x 5 x 4 for some as yet unknown multiplier a However since it was given that f 4 160 we substitute 4 for x and 160 for f x and solve f 4 160 a 4 4 5 4 4 f x 5 Step 4 Using all the information we found we can now write the full expression x 4 and since f 0 0 then f x has the factor

Solve 2 34 32 6 2y 22 0 2 3

Given the following functions find each f x x 3x 4 g x x 4 f g x f g x f g x

Question Consider the region bounded by the graphs of y x y 17 and x 6 in the first quadrant What is the volume of solid obtained by rotating this region about the line x 2 Select the correct answer below 17 2 O af Ty 6 16 dy JU 17 Ty 4 36 dy 17 OT Ty 2 16 dy LF 01 26 14

Find the magnitude of the vector given below Also find the measure in degrees of the acute angle formed by the vector and x axis Do not round any intermediate computations and round your responses to 2 decimal places y 0 a magnitude of the vector b 0 X

The graph of y f x is given Graph the function y x 2 3

Convert the measurement 13 mm cm

8 Write an equivalent expression over the given domain x 6 for all x except 3 and 5 x 5

17 through 2 4 and 1 3

2 a 4 a 7 7 a a 4

5 x 25 x 8x 15

JE

y 7y 12 y 3y

3 4 5 6 7 8 9 12 8x 1 x 2 3 4 3 1 10

Classwork Homework Name 1 Slope Intercept Form y mx b Determine the slope and y intercept for each graph Write the equa 2 slope slope y intercept y intercept Qyinkansola Alavan equation 6 54 3 2 1 slope C 1 Linear Functions review all t Wi 1 2 equation 6 5 151 1 5 y 2x y 4 3 2 1 slope 1 2 3 4 5 6 1 2 Write each equation in slope intercept form identify the s Clearly mark at least three points on each line Show your 4 y 6 5 x y 4 3

O 32 t 11 x x 6 X Type a response

13 2x x 4 What is the extraneous solution to this problem Type a response

3 10 4 5 6 7 3 61 x 5 2x 8 When you solve this problem what is the value of each side of the equation ROUND YOUR ANSWER IF NEEDED 4 24 13 8 9 4 10 11 12 13

m 4 12 8x 1 x 2 3 4 3 1 K 8 9 10

You create a post on a social media site and tag six friends In the second round each of your friends tag six people and the process continues a Write a function that represents the number of people who are tagged in the nth round A 9 b In which round will 7776 people be tagged Rou

Listen Determine whether the table represents an exponential growth function an exponential decay function or neith x 1 2 3 4 y 3 11 19 27 O exponential growth function O exponential decay function neither

Part A Your grandmother opened an account when you were born with 1000 The account earns 3 interest compounded quarterly How much money will be in the account when you turn 18

5 1 Two numbers multiply together to equal 64 but add together 12 What are the two numbers Select Select 16 32 8 and Select 4 Select

The surface area of a right circular cylinder is given by the polynomial 2xrh 2xr where h is the height r is the radius of the base and h and r are given in the same units A beverage can has height 5 9 in and radius 1 4 in Find the surface area of the can Use a calculator with a key or use 3 141592654 for The surface area of the can is in GILB

Given the following data X 65 V 95 x 325 Zy 475 Exy 308 the value b 1 5 slope in the linear regression equation a bx find Ex Select one a 21145 b 21125 c 21155 d 21135

If A B are symmetric matrices and AB BA then AB is also symmetri Select one True

W is the set of all vectors in R2 whose second component is the cube of the first Select one O O O O a W is subspace because it s not closed under addition b W is not subspace because it s closed under addition c W is subspace because it s not closed under addition d W is not subspace because it s not closed under addition

If A is 4x3 matrix and Nullity A 0 then Rank A 3 Select one True False

if A is singular find value of x 12 x 1 1 1 2 1 1 Select one ooo b 1 C 1