Quadratic equations Questions and Answers

Consider the following function f x 3 x Step 1 of 4 Determine the more basic function that has been shifted reflected stretched or compressed Answer g x

Question 1 of 11 Step 1 o Consider the following graph of g x Write a formula for g x that describes the transformations performed on the function 10 5 10 5 S Enable Zoom Pan 5 10

By EZ a B A Bx GIVEN a 44 B 4 4 km FIND A B B

The given equation has a solution r in the interval 2 rs 1 Approximate the solution correct to two decimal places 4x x 3x 3 0 TR Round to two decimal places as needed

Question 16 Solve the equation by using the Square Root Property for Equations 2y 2 54 y

Factor out a factor with a negative coefficient 36r 4 s 3 28r 2 s 4 16rs 5

A parabola can be drawn given a focus of 10 7 and a directrix of r 6 What can be said about the parabola FL 104

Carrie shoots a basketball at an angle of 35 from the horizontal It leaves her hands 6 feet from the ground with a velocity of 24 ft s Step 1 of 2 Construct a set of parametric equations describing the shot Round all final values to the nearest tenth Answer

map of the sci to find the trains nature dinosaurs geology and planetarium exhibits Each unit represents one meter What is the area of the science center elopna bliud 8 Draw and label the coordinates of a rectangle on the coordinate plane that has quare an area of 20 square units aths OF Ay 61 Panoo 26ri eroj bre S bne STERN 2 2 8 aplito 9 BL pl PT ES TI a F t

ell whether each sentence below is true or false 1 1 Synthetic division will only work if the problem has a 0 remainder

How many pounds of the 50 mixture should the farmer in 9 use Select one O a 126 7 lb O b 360 lb O c 95 lb O d 23 3 lb

4 An interesting thing happens when you multiply two conjugate binomials Conjugates have the property of having the same terms but differ by the operation between the two terms in one case addition and in one case subtraction Multiply each of the following conjugate pairs and state your answers in standard form The first is done as an example a x 3 x 3 b x 5 x 5 c 10 x 10 x x x 3 3 x 3 x 3x 3x 9 x 9 d 2t 3 2t 3 e 5t 1 5t 1 f 8 3t 8 3t

Write tan sin 1 2 as an algebraic expression in u

Taylor has 25 coins consisting of pennies and nickels The sum of his coins is 57 How many of each coin does he have Select one O a 8 pennies 17 nickels O b 7 pennies 5 nickels O c 16 pennies 9 nickels O d 17 pennies 8 nickels

3 Never forget that squaring a binomial is also a process of repeated distribution Write each of the following perfect squares as trinomials in standard form a x 3 b x 10 c 2t 3

get sq perfect squares as trinomia a x 3

Multiply the rational expression Simplify the product if possible x 2 12x 35 x 2 4x 21 x 3

The size P of a certain insect population at time t in days obeys the function P t 7000 a Determine the number of insects at t 0 days b What is the growth rate of the insect population c What is the population after 10 days d When will the insect population reach 840 e When will the insect population double a What is the number of insects at t 0 days insects b What is the growth rate of the insect population 0081 c What is the population after 10 days Approximately insects Do not round until the final answer Then round to the nearest whole number as needed

t II Find the other roots If one of the roots of the polynomial equation x 5x 14 0 is 2 find the other root If one of the roots of the polynomial equation x 13x 12 0 is 4 find the other roots and

rt I Determine the number of roots and what are the roots of the 1 x 4 x 3 0 How many roots are there in this equation What are the roots polynomial

1 Use the rules for order of operations to evaluate the following expression Write the solution as a mixed number or a fraction in lowest terms A 17 25 813 4 17 4 5 4 5 2 5 2

Decay Question 6 4 5 42 re 0 0 of 12 points O Points 0 of 1 A logistic growth model for world population f x in billions x years after 1960 is f x this model what is the limiting size of the population that Earth will eventually sustain 1 4 23e The limiting size of the population that Earth will eventua sustain is Type an integer or a decimal billion 12 73 0 026x Save According to

Decay Part 1 of 3 109 000 1 4500e weeks after its initial outbreak in a particular community The logistic growth function f t HW Score 0 0 of 12 points O Points 0 of 3 describes the number of people f t who have become ill with influenza t a How many people became ill with the flu when the epidemic began b How many people were ill by the end of the fourth week c What is the limiting size of the population that becomes ill a The number of people initially infected is Round to the nearest whole number as needed Save

Decay Question 4 4 5 29 It will take approximately Round to one decimal place Use the exponential decay model A Aoekt to solve the following The half life of a certain substance is 22 years How long will it take for a sample of this substance to decay to 74 of its original amount years HW Score 0 0 of 12 points O Points 0 of 3 percent per year percent Save for the sample of the substance to decay to 74 of its original amount

The symbol log x indicates that it is a base 10 logarithm The solution of the equation log 4 log x 3 is an integer What is your answer Give the number as an integer only

Given p x 4x 1 and q x x 3 find each 3 Excluded value s of 0

19 log 5x log 5 4 20 log 3x log 3 5

Question 5 Solve for X log x log x 10 log x 18 O X 2 X 9 Ox 2 and x 9 O no solution exist

Multiply the polynomials Simplify completely 11x 9 x 3x 2 x

Multiply and simplify completely 4m 2m 7 8m 1

Multiply and simplify completely 9p p 9 10p 3

Multiply using the FOIL method Simplify completely 2xy 12 3xy 2

Multiply the binomials and simplify x 11 x 11

Multiply the binomials and simplify x 5 x 6

Simplify the expression by using the distributive property 5 3z 7

Alfredo Gutierrez bought 2 000 shares of a phone company s stock at 36 50 per share He sold his stock at 48 25 per share Each transaction paid a sales commission of 49 95 plus 0 02 per share a What was the net amount of the sale b What was the profit or loss from the sale

Let U a b c d e f 7 8 9 10 11 12 List the members of the set X nY using set braces X a b c 7 8 9 and Y b d f 8 10 12 and the members of the set Y are The members of the set X are Use a comma to separate answers as needed X nY 0 Use a comma to separate answers as needed

Use A 4 6 7 8 9 and B 1 2 7 9 to find the set An B AnB Use a comma to separate answers as needed

Which equation can be simplified to find the inverse of y x x y 1 1 7 1 7 O x y 7 O x y 7 O

Which of the following describes the graph of y 4x 36 compared to the parent square root function O stretched by a factor of 2 reflected over the x axis and translated 9 units right stretched by a factor of 2 reflected over the x axis and translated 9 units left Ostretched by a factor of 2 reflected over the y axis and translated 9 units right Ostretched by a factor of 2 reflected over the y axis and translated 9 units left

Which equation is the inverse of 2 x 2 2 8 7 y O 2 x 2 8 7 y O y x x 6 Oy 2 28 4x Oy 2 28 4x

Which could be the function graphed below f x x 2 Of x x 3 1 Of x 2x 4 Of x x 1 8

El 10 12 14 16 9 10 11 12 13 10 12 Which symbol inserted in the blank will make the above statement correct O A Vorn OB n OC U

mine if the statement is true or false E 1 5 6 9 10 se the correct answer below True False

Which equation can be rewritten as x 4 x Assume x 0 O x 2 X O x 2 X O x 4 X x 16 x

Solve the system of equations If the system has an infinite number of terms of the parameter z x x 2x X y 2 3z 5 20 3z 7 Y 5y 6z Y

Solve the system x 1 5 2 1 1 1 2y z 5 2 y z 3 z 4 If there is one solution enter your answer as a point x y z O One solution O No solutions Many solutions

Solve this system of equations 3x 2y 1x 4y X y 14 14

Solve this system of equations 2x y 4x 4y 3 4

Find all solutions of each of the following equations giving your reasoning 3 2 cos s tan t 2023 1 2 sin u sin 2u