Quadratic equations Questions and Answers

1 Is the graphed function continuous at 2 What about 2 If it is not continuous give which of the thre properties of continuity fail 5 y 5 5 5

Ex Determine over which interval s the graph is increasing and decreasing 3 Note You should also be able to write the intervals of increase and decrease in interval notation What would the answers above be in interval notation Pause the video at time mark 03 52 We will look at two methods for graphing parabolas 1 Write the function in vertex form also called standard form 2 Use the vertex formula

Use the graph of the function f to solve the inequality a f x 0 b f x 0 6 x 3 2 x 2 y 0 a The solution set for f x 0 is Type your answer in interval notation b The solution set for f x 0 is Type your answer in interval notation

Shown is the graph of a parabola y f x with vertex 2 1 What is te vertex of the parabola y f x 1 A

Use the graph below to write down the rational function f x represented in it y f x

If log 2 x and log 3 x and y a logo 24 b log 1296 c logb 27 d log 27 log 2 y evaluate the following in terms of

Which graph is defined by the function given below y x 3 x 4 10 10 10 A 10 10 OA Graph A OB Graph B OC Graph C D Graph D 10 B 10 10 10 C 10 10 10 D 10

Find the measure of the angle 55 Select one O a 210 degrees O b 125 degrees O c 180 degrees O d 235 degrees

Sketch the graph of y tan 20 a b 2 2 7 NAA 2 IN 57 37 2 2 A C d 2 N 2 L 444 HN 522 KIN C 27 At 37 2 NEA 2 A

Sketch one cycle of the sine curve y 3 sin 40 a b 2 2 L 19 2 A 15 2 7 64 0 C d N 0 2 7 2 54 M T 27 23 9 64

Ex Solve the inequality Draw a number line graph of each solution and give the interval notation 3 2x 9 Graph 10 7 12

Use cylindrical coordinates to calculate SSSw 2 dv av W 2 25 0

The graph below represents the grades for English and History tests There appears to be a strong positiv correlation Based on this graph if a student has an 90 in English he she is likely to have a in Hist 100 80 60 40 70 73 73 70 98 93 90 86 86 90 70 93 80

20 10 0 20 10 20 Choose Choose Weak Positive Correlation Strong Negative correlation Weak Negative Correlation Strong Positive Correlation

Determine whether the following function is one to one f x 6x 6 OThe function is one to one The function is not one to one

Expand the logarithm as much as possible Rewrite as a sum difference or product of logs Preserve order logb 15 log log Preview syntax error Preview

Use the like bases property to solve the equation 10 1 10 18 7 2 Preview

Match each linear equation with its graph a Equation y 5x 3 y 4 vy x 3 y 3x y 3x Graph Color a red b black c blue d green e purple

The table shows the number of books read by students over the summer and their grades for the following semester Books vs Grades Books 0 0 0 0 1 1 1 2 2 3 5 8 1014 201 Grades 64 68 69 72 71 74 767579858691949998 The data demonstrates Hint Graph the data to positive negative no correlation

5 8 In the figure W is the point of intersection of the angle bisectors ZABC y ZBCA of the AABC Show that m BWC mZBAC 2 90 A W

Books vs Grades Books 0 0 0 0 1 1 1 2 2 3 5 8 10 14 20 Grades 64 68 69 72 71 74 76 75 79 85 86 91 9499 98 When graphing this data on a coordinate plane the Books will be the Y axis and the Grades will be on the axis

point is the function a power function It it is write it in the form g e k and enter exact values for and p it is not a power function enter NOME in both blanks Do not leave any blanks empty 8 help actions

A child swings on a playground swing set If the length of the swing is 5 m and the child swings through an angle I of what is the exact arc length through which the child travels 9

The table below shows the number of each type of cookie in dozens that Karin sold in one work to two coffee shops Chocolate Chip Oatmeal Peanut Butter Mugsy s Coffee Shop 6 9 6 The Coffee Club 3 4 10 Kann s profits on one dozen cookies is 6 75 for chocolate chip 4 60 for oatmeal and 7 25 for peanut butter Complete parts a and b a Write a row matrix P that represents the profits for each type of cookie Maintain the ordering of cookie types from the table Type an integer or decimal for each matrix element 83 b The matrix 5 9 4 represents the information in the table Use the matrices S and P to find the total profit from each coffee shop 6 10 PS P S S P n integer or decimal for each matrix element

3 7 points Let A 1 1 4 Find a singular value decomposition of A

Find the amplitude 2 2 Select one O a 4 O b 5 O c 2 O d 3 A 6

Use the definition of a logarithm to solve the equation Answer DNE if no solution exists In 52 ln 2 3x 2

2 20 Points The population P of a town increases as the following equation P t 50ekt If P 3 90 what is the population size at t 5 2 20 Points The population P of a town increases as the following equation P t 50ekt If P 3 90 what is the population size at 5

Find an expression for the perimeter of the figure x 5x 1 Triangle 4x 2 x x 15

Use the definition of a logarithm to solve the equation BORN VENETRES ESPERT L PRES EN PASS DESENAL SEELANDER BELYDE BEN HERREYORUUSIAKKER 3 log x 9 En Sony ERMAL FAS EA ATAKENNEUL BETALICA CORNETA Cube DocesDY CENTRE WHERE SHEN S HEMAT PORTRETERESTPRESENTE AMIENTUELVEL CATEGSENT 1 SOESTIV C OPERAT MEANS OVE SINABI x GLEBONT PER

pive for Solve for if 16 sin 0 7 23 and 0 0 2T Select the correct answer below 0 0 16 sin 7 23 and U 57 3 7 and 0 00 5 only 9 00 only 2 0 0 3 only 2 57 6 21

1 1 The formula 1 x 22 models the percentage of households with an interfaith marriage 1 x years after 1989 The formula N x 9 1989 Answer parts a d below a In which years will more than 33 of households have an interfaith marriage After the year CLO

Graph the system of equations and state whether the system is consistent inconsistent or dependent and whether the system has one solution no solution or infinite solutions If you notice the two lines are the same only graph the line once x 3y 2x 6y 8 16 7 6 5 4 3 2 1 Clear All Draw 6 ONo solution 5 4 3 2 1 1 2 56 N consistent inconsistent depedent O One solution x y 2 3 4 5 6 7 Preview

The range of the function f x x 4 5 is 5 True False

How many polygons can you find

Evaluate the function Round your answer to four decimal places if necessary f x 3 for f 2 33x 3 f 2 Preview

Find the length of the indicated arc Round your answer to the nearest tenth Do not include a unit labe 2 m 3g

Consider the graph of f x below 9 8 9 8 7 6 4 0 3 2 10 12 5 6 7 8

8 Now find a formula for the graph that you see and describe how to get this graph from a common graph through transformations 7 H 40 30 20 10

Find the measure of the missing angles b 0 C mun ntokka 0 bc 85

Find the length x X A 39 Round to the nearest tenth as needed X B 30

Suppose that the revenue R in dollars from selling x cell phones in hundreds is R x 1 5x 208x The cost C in dollars from selling x cell phones in hundreds is C x 0 05x 2x 50x 750 a Find the profit function P x R x C x b Find the profit if x 18 hundred cell phones are sold c Interpret P 18

Find the following Assume that x can represent any real number Use absolute value notation when necessary 6x 9

Draw the graph of the function f x 3 3 x 1 Select one O a O b D

rigonometry 5 4 3 3 8 25 20 15 10 5 41 21 S 10 15 20 25 1 4 1 2 3 what is the equation of this graph 4 5 x

A manufacturer in Johannesburg operate nonstop for 24 hours A workday is divided into 3 shifts The following table shows the number of absentees in a five day week Day 1 2 3 4 5 Shift Early Late Night Early Late Night Early Late Night Early Late Night Early Late Night Find the values of x and y A x 59 y 24 B x 59 y 24 3 C X 40 y 24 D x 40 y 24 3 Number of absences 14 12 29 15 11 31 17 16 32 18 18 37 21 21 38 Three point total 55 56 55 57 64 65 66 68 73 76 79 80 Three point moving average 18 3 18 7 18 3 19 19 7 21 3 21 7 22 22 7 y 25 3 26 3 26 7

3 Find the distance between B and C 60 20 C B

In AABC find each value a sin A b sec A d csc B e sec B a sin A c cot A f tan B Type an integer or a simplified fraction B 51 24 1 A 45 L

A conical cup is made from a circular piece of paper with radius 24 cm by cutting out a sector and joining the edges as shown below O 24 cm 24 cm h r 24 cm In this exercise we find the volume of the conical cup for any angle 8 a Find the circumference C and radius r of the opening of the cup and the height h of the cup to show that the volume of the cup as a function of E V 0 575 0 41 02 0 0 2m

of the data represented in the histogram below as either left skewed right skewed or zere skewed symmetrical Select one O a Right Skewed Ob ft Skewed