Quadratic equations Questions and Answers

a Rewrite the equation 3x y 5 0 in slope intercept form b Give the slope and y intercept c Use the slope and y intercept to graph the linear function a The slope intercept form of the equation is Simplify your answer Use integers or fractions for any numbers in the equation b The slope of the equation of the line is and the y intercept is Type integers or fractions c Use the slope and y intercept to graph the line Click to enlarge graph 10 6 4 b 10 8 6 4 2 2 4 6 10

Let f x 6x 5 and g x Find f g x f g x fg x and 1 f g x 6x 5 Simplify your answer X f g x fg x 1 X 6x 5 1 X 1 X 6x 5 X Simplify your answer Simplify your answer x x 6x 5 Simplify your answer 5 The domain of f g is 6 Type your answer in interval notation The domain off g is 5 6 Type your answer in interval notation The domain of fg is Type your answer in interval notation x Give the domain of each

Let f x 6x 5 and g x Find f g x f g x fg x and f g x fg x 9 X 6x 5 1 X 6x 5 X Simplify your answer x x 6x 5 Simplify your answer 5 The domain off g is 1 X Simplify your answer The domain off g is Type your answer in interval notation 5 6 Type your answer in interval notation The domain of fg is Type your answer in interval notation x Give the domain of each

Let f x 6x 5 and g x Find f g x f g x fg x and X f g x Simplify your answer x Give the domain of each

X to 10 S2 a Domain B b Range 6 Type your answers in all of the blanks and submit 2 4 2 enter any spaces in your answer Fill in the blanks with the interval notation that represents the domain and range of the function given in the graph To indicate enter the word infinity To indicate enter the expression infinity Use the appropriate symbols on the endpoints Do not 4 Write your response mere 6 x Write your response here

Refer to the graph of the quadratic function h shown to the right How many real solutions does h x 0 have How many nonreal complex solutions does it have How many real solutions does h x 0 have One Two None How many non real complex solutions does it have O Two O One Nono hint

Find fog x and gof x f x 7x 6 g x x fog x Simplify your answer

Click on the graph of the function f x X 1 3 A B 4 C D

For f x 8x and g x x 6 find the following functions a fog x b gof x c fog 2 d gof 2 a fog x Simplify your answer b gof x Simplify your answer c fog 2 d gof 2

3 For y 1 b cos x with 0 x 2 and 2 b 6 where doe the lowest point of the graph occur What happens to the graph as b increase

X X 2 Let f x x 1 x 3 a The degree of the function is Type your answer here Type your answer here Type your answer here Type your answer here b Use a graphing calculator to find the coordinates of the turning point containing the relative minima from left to right turning point s Type your answer here Type your answer here so the graph of the function has at most c Use a graphing calculator to find the coordinates of the turning point containing the relative maximum Type your answer here and Type your answer here

e Assume a member is selected at random from the population represented by the graph Find the probability that the member selected at random is from the shaded region of the graph Assume the variable x is normally distributed The probability that the member selected at random is from the shaded area of the graph is Pregnancy Length in a Population of New Mothers 282 x 293 242 282 Pregnancy length in days 269 a 10 Round to four decimal places as needed 293

X X Fill in the blank with the appropriate word If a rational function is undefined at the number h then the graph of the rational function has a vertical Write your response here at x h

1 point Let f x be given by the large graph to the night On a piece of paper graph and label each function listed below Then match each formula with its graph from the list A I below By 2f x Hy 2f z G y f x 1 1 y 31 2 A y f x1 y 1 f x 3 A MAA yer u NA B D VMW E y f x F LL y

Find the equation of a plane that is perpendicular to the vector 1 3 2 and passing through the point 3 1 5 The plane is given by

Students in a fifth grade class were given an exam During the next 2 years the same students were retested several times The average score was given by the model f t 95 10 log t 1 0 t 24 where t is the time in months Round answers to 1 decimal place a What is the average score on the original exam b What was the average score after 12 months c After how many months does the average score drop below 83 months

Relative Speed m s Mass A 11 51 BE ZI 6x w SS SA Animal Fallow deer Desert warthog 6 36 bu 9 9 227 10 97 3 03 5 4 3 8 3 6 1 79 OOE 550 Mountain goat Antelope Black wildebeest Camel 598 1075 1200 European bison Giraffe 0002 Black rhinoceros White rhinoceros 7 1 18 1 4 1800 Hippopotamus 1000 6000 Asian elephant African elephant Source Journal of Experimental Biology 205 2097 2900 Shutterack a Examine the data and explain why an inverse variation relationship might best model the situation As the mass of the animal increases the relative running speed generally decreases at a decreasing rate b Use a graphing calculator to find a power function model Round your values to two decimal places v m Use the model to describe the relationship between maximum relative running speed and body mass of these animals As the mass of the animal increases the relative running speed decreases c Use the power regression model to determine the mass of an animat with a relative running speed of 8 16 meters per second Round your answer to two dec

a through j 12 17 0 15 11 3 9 3 7 0 Ay 5 5 2 0 2 1 1 1 4 2 3 3 6 0 y f x 15X O Q

Click on the center of the graph of the given function f x 0 5 x 2 x 1 x 4 A C D 41

Solve the following logarithmic equation In x 9 In x 3 2 ln x Select the correct choice below and if necessary fill in the answer box OA The solution s is are Simplify your answer Type an integer or a fraction Use a comma to separate answe B The solution is not a real number

Find the slope of the line in the graph 7 6 5 4 3 2 1 6 5 4 3 2 1 7 1 2 3 4 5 6 7 3 4 Preview 5 6 7

he matrix A 281 1586 1301 2711 has non real eigenvalues Find P and C so tha m a b PCP 1 where P is invertible and C is of the form

Refer to the graph of the equation y sin x on the interval 0 4 Find all values of x such that a y 2 2 b y 2 2 and c y

X X 2 Fill in each blank with the appropriate number or word using the given function P x 3x 1 1 4x 2x 1 a The leading coefficient of Pis Type your answer here b The degree of P is In the following blanks enter up or down c The graph will go Type your answer here d As X y In the following blanks enter positive or negative e As X y Write your response here Write your response here Write your response here DEN POSTRIER to the right and infinity infinity Write your response here to the left

Use the function f x As X 00 y 2 X 3 2 to determine the information

Use the image below to match cech graph to its correct description Graph A Graph C f Zeras of 2 1 0 1 and 2 cech with multiplicity 1 Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE Zeras of 2 mult 1 1 mult 1 0 mult 2 1 mult 2 and 2 mult 1 Zeroa of 2 mult 1 1 mult 1 6 mult 2 1 mult 1 and 2 mult 2 Zeroa of 2 mult 1 1 mult 2 0 mult 1 1 mult 2 and 2 mult 1 GraphB Graph D Graph C Graph B Graph A Graph D

4 Find the inverse of the following functions or explain why no inverse exists a f x 2x 10 x 1 b g x 2x 3 c h x 2x 3x 2 d r x x 1

Using the points segments and lines in the figure list all parts of the circle a center b radii c diameters wo d chords e secants f tangents E A D B C

The graph of the relation y 1 is shown Use the graph to find the domain and range and indicate whether its a graph of a function Domain 6 54 4 3 2 7 6 5 4 3 2 1 Range Is it a function Select an answer No 123 2 5 6 1 2 3 4 5 6 h Preview Preview

Read the graph to determine if It goes up or down to the left and right Then select the statements that are true about its and behavior Assume the graph extends Infinitaly In each direction 2 NJ 6 b 5 As X 00 y xc Multiple anawera Multiple enawers are accepted for this qucation Select one or more anawers and submit For keyboard navigation SHOW MORE Az X y C AG X y 4 3 1 2

A polar curve is represented by the equation r 3 3sin 8 Part A What type of lima on is this curve Justify your answer using the constants in the equation Part B Is the curve symmetrical to the polar axis or the line Justify your answer algebraically Part C What are the two main differences between the graphs of 3 3sin A and re 83000 83

For questions 9 11 identify the domain and range 2 2 20 18 16 14 12 10 84 1 2 3 4 08 7

Find the domain and range of the relation graphed below foa q 5 4 Domain 21 723 2 3 4 n 1 2 3 4 5 Preview Range NOTE If you do not see an endpoint assume that the graph continues forever in the same directi Preview Entry example 2 3 or 00 5 Enter 99 for negative infinity and oo for infinity

Find the slope of the line in the graph 7 6 5 4 3 2 1 Slope 7 6 5 4 3 N 2 2 2 3 6 Lo m Preview ST 6

Type your answers in all of the blanks and submit X X 2 Find the requested information for the polynomial 4x x 6 x 1 a The leading coefficient of the polynomial is Type your answer here b The leading coefficient is Write your response here positive negative c The degree of the polynomial is Type your answer here d The parity of the degree is Write your response here even odd

State the implied domain of g x 9x 4 Give an exact answer not a rounded decimal using proper notation Use the wor infinity as necessary rather than the symbol

The graph of the function g x is shown below Use the graph to answer the following questions Evaluate g 1 Evaluate g 4 Evaluate g 3 7 6 5 Evaluate g 0 fo LAS 7 6 5 4 3 2 1 1 CN 2 2 3 4 5 6 1 74 1 2 3 4 5 6 g 1 g 4 9 3 g 0

For the following exercise use the function f represented in the table below a Evaluate f 0 f 0 b Solve f x 77 x f x 0 27 1 71 2 34 3 4 35 5 5 77 6 20 7 8 43 52 9 54

Problem 35 Find p P3 R such that p 0 0 p 0 0 and 12 3a p x da is as small as possible

3 Solvex x 16x 16 0 algebraically using the chart method x 1 x 16 0 x 1 x 4 x 4 0 x 1 x 4 x 4 6 Am 12 4 6 2 x 41 6 6 X 4

The graph shown below is what basic function with possibly some transformations applied constant function f x a linear function quadratic function f x ax b even power function f x ax bx c f x x n is even

Find the exponential function f x Ca whose graph is given below y YA f x 0 1 6 3 24 X

1 15 points Consider the plane region with point masses as indicated Find the center of mass of the region mass weight kg location 1 2 1 4 3 0 4 2 7721 m2 7713 m4 3 5 4 2 12

An incomplete graph of the polynomial function f x x 4x 15x 18 is shown on the right a Find all zeros of the function b Without using a graphing utility draw a complete graph of the function a The zeros are 5 0 1 by 35 30 5 G

6 pts Solve the inequality Draw a number line graph of the solution and give the interval notation 4 3x 2 Graph 10 8 6 4 2 0 2 6 8

The graph shows a region of feasible solutions Use this region to find maximum and minimum values of the objective function z 0 20x 0 80y Select the correct choice below and if necessary fill in the answer box to complete your choice A The maximum value is 7 2 B There is no maximum value Select the correct choice below and if necessary fill in the answer box to complete your choice A The minimum value is BLEER 10 04 0 ON 10 The coordinates of the corner points are 0 0 0 9 4 8 7 5 8 0

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