Quadratic equations Questions and Answers

Factor by Grouping must have 4 or more terms Factor by pairing 2 terms together and factoring out a GCF Ex Factor x x 3x 3

f 8 3

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b 72

8

a1 0 123 13 A az ay 39 au

03 MC Given f x is true x 7 x 3x 28 f x is positive for all x 7 f x is negative for all x 7 f x is positive for all x 4 which of the following O f x is negative for all x 4

Given f x true 10 x 7x 30 which of the following is f x is negative for all x 3 f x is negative for all x 3 f x is positive for all x 10 O f x is positive for all x 10

The price of a jumper is 29 It is reduced by 15 in a sale What is the new price of the jumper Give your answer in pounds

Use the pair of functions to find f g x and g f x Simplify your answers f g x ab ab a sin a 8 sin a 8 f x x 6 g x x a 25 AS

Question Determine the domain on which the following function is decreasing

Paul considers investing 8 000 in three different accounts for 6 years Option A 5 simple interest Option B 4 5 interest compounded continuously Option C 4 75 interest compounded yearly After 6 years Option B to the nearest dollar will be worth more than Option A and less than Option C linear quadratic are exponential constant Option A is a function while Options B and C functions While the function gains value the fastest initially over time the functions will alue faster

f x is 4 The roots of the equation f x 0 are 8 5 1 and 2 Which graph could be the graph of f x O 10 8 6 4 10 8 250 200 150 100 50 50 100 150 200 250 250 200 150 100 50 350 100 150 200 250 2 4 6 8 10 2 4 6 8 10 O 10 8 6 4 10 3 4 250 200 150 100 30 100 150 200 250 50 250 200 150 100 50 30 100 150 200 250 2 4 6 B 10 8 10 X

Which graph represents the function f x x O 10 8 6 4 100 80 60 40 20 20 40 60 80 100 100 80H 60 40 20 10 8 6 4 20 2 4 40 60 80 100 2 4 6 6 8 10 8 10 X 14r3 612 84x 36 100 80 60 40 20 10 8 6 4 2 320 40 60 80 100 y 100 80 60 40 20 10 8 6 4 20 40 60 80H 1004 k 2 4 6 4 6 8 8 10 X 10

The degree of the polynomial function f x is 3 The roots of the equation f x 0 are 2 0 and 3 Which graph could be the graph of f x O 10 24 10 8 6 4 2 ON 4 6 8 10 y 10 8 6 2 N 10 8 6 42 6 do d 8 10 2 4 6 8 10 24 6 8 10 X O 10 8 6 4 2 6 8 104 8 6 10 8 6 4 2 10 8 6 4 10 9 4 2 10 6 8 y 2 4 6 8 10 2 46810 Se

Which graph represents the polynomial function f x x 4x 15x 18 P x 45 40 35 30 25 20 15 10 5 A5 194 15 20 25 30 f x 80 75 70 65 60 55 50 45 MO As 30 20 15 10 20 15 10 8 7 6 5 4 3 6 10 16 204 25 A N 35 30 10 10 15 20 25 30 35 40 20 15 45 x 50

Which graph represents the polynomial function g x x 5x 12x 36 O 50 40 30 20 10 0 10 20 30 40 50 50 40 30 20 10 0 10 20 p 40 8 50 O 2 f N 50 40 30 20 10 0 10 20 30 40 00 50 40 50 30 20 10 0 10 20 50

Find mZEOF for Oo E

Complete the steps to solve the inequality 3 72 y 1 a Multiply each side of the inequality by 2 and enter the simplified result Type your answer here b Isolate the variable term on the right side and enter the simplified result Type your answer here c Solve the inequality Write your response here Type your answer here IV y Write your response here Type your answer here

How many complex roots does the equation 0 424 23 5x 3 have O 3 04 5

9 4 3 2 A 4 2 3 3 2 C 4 B 10 5 5 12 4 2 7 D 10 10 2 3 4 3 3 5 4 6 3 A 23 B 8 2 15 C 2 D 4 5 2 10

How many complex roots does the polynomial equation have 3x4 7x 17 0 02 O 3 04

What is the completely factored form of f x x 4x 7x 6 o f x x 2 x 1 i 2 x 1 i 2 O f x x 2 x 3 i 10 x 3 i 10 o f x x 2 x 3 i 10 x 3 i 10 O f x x 2 z 1 i 2 x 1 i 2

The graph below shows how the average beak size depth in a population of ground finch shifted during particularly wet and dry years 1977 1980 and 1982 were all drought years 1984 was a wet year During drought years all the seeds were large and tough to open This meant that birds exercised their beaks more making the beaks stronger beak depth mm 10 5 10 0 9 5 9 0 0 1977 1980 1982 1984

Which answer best describes the complex zeros of the polynomial function f x x x 6x 6 O The function has three real zeros The graph of the function intersects the x axis at exactly three locations O The function has one real zero and two nonreal zeros The graph of the function intersects the x axis at exactly two locations O The function has one real zero and two nonreal zeros The graph of the function intersects the x axis at exactly one location The function has two real zeros and one nonreal zero The graph of the function intersects the x axis at exactly one location

The number of books donated to a library is increasing by 25 each month Initially there were 80 books donated to the library There were 100 books donated at the end of Month 1 How many books are expected to be donated to the library at the end of Month 10 Round the answer to the nearest whole number Enter your answer in the box

Which equations represent exponential growth Which equations represent exponential decay Drag the choices into the boxes to complete the table Exponential Growth Exponential Decay

Alicia invested 32 000 into an account earning 3 annual interest compounded quarterly She makes no other deposits and does not withdraw any money What is the balance of Alicia s account in 7 years O 32 426 67 O 39 446 78 O 43 099 36

2 Grace and Kaitlyn are trying to find three consecutive integers such that the square of the second number plus the product of the first and third is a minimum Help them find the number

What is the length of the arc on a circle with radius 16 ft intercepted by a 60 angle Use 3 14 for T Round the answer to the hundredths place Enter your answer in the box ft

An angle in standard position measures In which quadrant does the terminal side of this angle lie O Quadrant I O Quadrant II O Quadrant III radians O Quadrant IV

Define the Fundamental Theorem of Algebra Part B Show that the Fundamental Th

What is the value of sin given that 3 4 is a point on the terminal side of 0 0 1 1 0 13 1 5 O C 335 4

One company s profit is modeled by a quadratic function with zeros 5 and 20 The point 8 72 is also on the boundary line Any values above the boundary line exceed the expected profits What is the standard form of the quadratic inequality represented by the description A O O C B COD y 2x 50x 200 y 2 50x 200 y 2x 26x 80 y 2x 26x 80

A soccer ball kicked from the ground with an initial velocity of 32 ft s is given by the function k t 168 32 When is the soccer ball moving through the air O A B C D t1 2 t 2 t1 4 t 4 t 0 t 2 t 0 t 4 1

Determine the solution for 2 3x 28 20 O A DOO OB O C D 7 4 4 7 x 4 or 7 00 7 or 4 00

Simplify the expression x2 17 O O O A B Oo C 2x7 7x x2 7 712

Choose the graph of y x 4x 5 O A O D O a C B L B H

Which expression is equivalent to x1 25 2 in simplified form O A O D 8 y Vys y

4a 49 O A 000 B O c OD 4 a 7 a 7 2a 7 2a 7 4a a 49 2a 7

Jeff used the equation 16 3 1 to calculate how many flowers were growing in his yard How many flowers did Jeff have growing in his yard O A B 5 O C 4 D 84 85

Where does the graph of the function h x 27x 125 cross the x axis A O O O B C D x 5 X 5 3 1 x 4 x 5 5 3

Select the quadratic inequality that represents the graph O A O B 10 5 20 10 3 24 10 4 30 0 V2 x 3 24 5

actor x x 12 O O O O A B O C O D x 6 x 2 x 3 x 4 x 3 x 4 x 6 x 2

Which polynomial function has a real root of multiplicity 2 O A y 4 12x 9x y 7 6x 3x y 4x 5x 5 y 4 92 B C

O A O Which of these polynomial functions is graphed below 8 6 4 2 O D B C D 40 Bet 20 50 10 LE 10 201 y 3 y x 27 y x 27 y x 3 2 2 6 8

Simplify the expression below 4 51 2 i O A DOO B C O D 13 6i 8 5i 13 6i

Write each expression in exponential form 14 7m A 3m C 7m Simplify 3 15 x 0 s A x C 10x 16 6b A 6b B 3 7 3 2 D m Write each expression in radical form B 27x9 D x6 B 4b m 3h

Newton s law of cooling states that for a cooling substance with initial temperature To the temperature T t after t minutes can be modeled by the equation T t T To T e kt where T is the surrounding temperature and k is the substance s cooling rate A liquid substance is heated to 80 C Upon being removed from the heat it cools to 60 C in 12 min What is the substance s cooling rate when the surrounding air temperature is 50 C Round the answer to four decimal places O 0 0687 O 0 0732 0 0813