Quadratic equations Questions and Answers

Suppose that f x x 6x 7 A What is the vertex of f B What are the x intercepts of the graph of f C Solve f x 7 for x What points are on the graph of f D Use the information obtained in parts A C to graph 2 f x x 6x 7

2 Find the following for the function f x 4x 2x 4 a f 0 e f x b f 4 f f x 2 a f 0 Simplify your answer b f 4 Simplify your answer c f 4 Simplify your answer d f x Simplify your answer e f x Simplify your answer f f x 2 Simplify your answer g f 3x Simplify your answer h f x h Simplify your answer c f 4 g f 3x d f x h f x h

x find the function g g x Simplify your answer Use integers or fractions for any numbers in the expression

2 Graph the equation and determine if it is a rational function Remember to solve the equation for y first 2x y 4 O yes O no

Graph the function f x x 1 2 5 by starting with the 2 graph of y x and using transformations shifting stretching compressing and or reflecting

10 Graph the equation using a graphing calculator Is the function an inverse or a direct variation 14 O direct O inverse y 3

4 Using the formula I PRT to find simple interest on an account find the amount of interest earned in 10 years if you deposited 2400 into a savings account earning 11 per year interest

The formula for the skin area of a human A in square meters is related to the height h of the person in centimeters and their weight w in kilograms by the following formula A 0 025h0 42 w Solve the formula for w

Determine the domain and range of the function 14 ROO CETTE O A domain 0 21 range 0 3 OB domain 0 3 range 00 21 OC domain 3 00 range 1 2 21 OD domain 2 2 range 1 3 0

Tickets to the zoo cost 12 for adults and 8 for children The school has a budget of 240 for the field trip An equation representing the budget for the trip is 240 12x 8y Here is a graph of this equation number of children 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 number of adults Select all the true statements M If four more adults go to the zoo that means there will be room for six fewer students If two more students go to the zoo that means there will be room for three fewer adults If ten students go to the zoo then 15 adults can go If 16 adults go to the zoo then 6 students can go oded 30 students could go to the zoo

Write v as the sum of two vectors one in Span u and one in Span u U3 4 Assume that u 4 is an orthogonal basis for R 5 5 5 5 U 5 1 5 U 1 5 U3 U4 5 5 5 V 5 6 3 3 V Type an integer or simplified fraction for each matrix element

The graph of y f 5x is obtained by a The graph of y f 5x is obtained by a up down to the left to the right shrink of the graph of y f x by dividing each of its Complete the sentence below Suppose that the graph of a function f is known Then the graph of y f x 2 may be obtained by a of f a distance of 2 units 6 shrink of the graph of y f x by dividing each of its horizontal A vertical Suppose that the graph of a function f is known Then the graph of y f x 2 may be obtained by a graph of f a distance of 2 units CILE Use the graph of y f x to graph the function g x f x 2 4 y f x X Q coordinates by 5 coordinates by 5 O A O C Choose the correct graph of g below shift of the graph OB shift of the

der the graph of the function y below 112 2 and f x 2 then 4 T 1

2 State an equation for the graphs below in factored form assume the leading coefficient for each is 1 marks 545 f x 12 12 f x f x 3 18 12 12 18 24 30 1 V 2 345

etermine the domain and range of the function Q a G AV OA domain 00 00 range 3 31 OB domain 00 00 range 3 38 OC domain 00 00 range 3 3 D domain 3 31 range 00 00

4 3 2 1 0 7 6 5 V 3 2 1 have 1 2 AWN 4 2 4 10 A A A A A A The graph above is a graph of what function

graphing by plotting po For the following equation find three ordered pair solutions by completing the table Then use the ordered pairs to graph the equation y 2x X 0 3 3 106 y 6 Use the graphing tool to graph the line Click to enlarge graph G Part 4 of 4 10 B 6 Ay 10 8 6 4 2 2 4 O Points 0 of 1 6 8 10 8 X 10 o

Rationalize the 94 7 2 To rationalize the denominator multiply by 1 using the conjugate of the denominator to write a symbol for 1 The conjugate of 7 2 is 7 2 Type an exact answer using radicals as needed Multiply by 1 using the conjugate of 7 2 94 94 7 2 7 2 7 2 7 2 Type an exact answer using radicals as needed To multiply the denominators use the equation A B A B A B 94 7 2 49 2 94 7 2 7 2 7 2 Simplify the denominator 94 7 2 94 7 2 49 2 Multiply

Number of Years 5 st m 2 1 16 20 O 25 28 18 OF 20 28 22 24 26 Average Daily Temperature The mean of the temperatures in the chart is 24 with standard deviation of 4 How many years had temperatur one standard deviation of the mean 30 32

tify the intercepts Ay 4 2 A A O G Select the correct choice below and if necessary fill in the answer box to complete your A The y intercept s is are Type an ordered pair Use a comma to separate answers as needed B There are no y intercepts

a f x x 2 4 A No Selution There is a horizontal shift 2 There is a vertical shift 4 Select all that apply horizontal shrink vertical shrink vertical stretch reflection in the x axis 77 Clear All unit s right unit s upward Fill WebAssign Graphing Tool Graph Layers Point 1 Point 2 Point 3 Point 4 Point 5

First find f g f g fg and g f x 4x 15x 54 g x x 6 f g x 4x 14x 60 Simplify your answer What is the domain off g 30 270 00 O 0 00 Then determine the domain for each function 0 00 30 30 00 29 270 00 30 0 00 f g x 4x 16x 48 Simplify your answer What is the domain off g fa x 0 00 0 00 00 18 u 158 00 5

94 7 2 What is the first step to rationalize the denominator Choose the correct answer below A Multiply by 1 using the conjugate of the numerator B Multiply by 1 using the conjugate of the denominator C Multiply by 1 using the opposite of the numerator OD Multiply by 1 using the opposite of the denominator To rationalize the denominator multiply by 1 using the conjugate of the denominator to write a symbol for 1 The conjugate of 7 2 is 7 Type an exact answer using radicals as needed Multiply by 1 using the conjugate of 7 2 7 0 94 7 2 7 2 Type an exact answer using radicals as needed 7 2 94

54 Write the equations for each of the following conics C b 10 a 10 O 10t 10 Ellipse where maior avis is vertical and 10 units long Ellinse has been translated 3 units un

Time s Velocity 22 m s None O 75 25 18 X The velocity at to 16 seconds estimated to be 30 429 m s using quadratic interpolation polynomial The value of X is most nearly to 35 m s B 36 m s 37 m s D 35 5 m s36 5mls was

Select one 01 What is the function graphed below 61 O 21 Ox 0 10 I can be any real number O x 0

Estimate the x and y intercepts from the graph B EN 02 x intercept s 9 8 7 6 3 3 ma 5 6 M 0 0 0 0 XA Write each intercept as an ordered pair Separate your answers using commas if necessary Select None if applicable ta PETE Nibnie

When you see two small markings on a segment it means that those two segments are congruent the same length 5x 7 3y x 3x 2y 9 Find an expression for the perimeter and combine like terms to simplify the expression Question Help M Moccagg

Estimated Monthly Salary 5600 5000 4500 4000 3500 3000 2500 2000 Estimated Monthly Salary 13 15 16 18 Years of Experience 19 21 How might the graph be misleading O The scale on the y axis overemphasizes the difference in salaries between different experien O The scale on the y axis underemphasizes the difference in salaries between different experie O The scale on the x axis overemphasizes the difference in salaries between different experien The scale on the x axis underemphasizes the difference in salaries between different experier

7 points Find all vertical asymptote s for Justify your answers using limits f x 15 7 x x 8 x 6

f x is a rational function given in both standard and factored forms Let f x 3 3x 2 x 4 4x 5 4x 5 Find 32 10 8 162 25 1 the domain in interval notation Note Use oo for 00 oo for Co U for union 2 the y intercept at the point 3 x intercepts at the point s 4 Vertical asymptotes at x 3 5 5 5 Horizontal asymptote at y 3 of OF mixed numbers are no

Solve the equation for g y gx a

Below is a graph of J 7 6 5 Sketch a graph of J 2 being careful to line up the x values 3 2 2 3 5 9 7 x

This is a 45 45 90 triangle What is the measure of x 8 X x X

Question 5 Given the accompanying graph of y f x sketch the graph of the followin y f x 5 4 10 4 4 2 46 20

3 Here is the graph of a quadratic function f 10 IN 3 4 5 6 2 0 3 4 6 0 A f x x 2 x 4 4 4 5 15 7 Select the equation that defines the function f 3 f x x 4 x 6 c f x x 4 x 87 D f x x 2 x 6

101 1 The graph of y f x is given below in its entirety 5 5 5 5 X a Find the exact value of f 2 b Find exact values if possible x if f x 2 e If the graph of g is obtained by moving the graph of y f x one unit down express g in terms of fand sketch the graph of g on the same grid d If the graph of h is obtained by expanding the graph of y g x vertically by a factor of express in terms of g and then in terms of f and sketch the graph of y h x on the sa grid e Sketch the graph of k x h 1 x on the same grid

T Let A and 2 2 eigenvectors J Find e At using its eigen

4 y 4sin 6x 2 Equation of Midline Amplitude Period Graph 3 periods 90 60 30 6 5 3 2 0 1 2 3 5 6 30 60 90 120 150 180 210 240 270 300 330 360 390 420

A consumer protection group randomly checks the volume of different beverages to ensure that companies are packaging the stated amount Each individual volume is not exact but a volume of iced tea beverages is supposed to average to 300 mL with a standard deviation of 3 mL The consumer protection group sampled 20 beverages and foun the average to be 298 4 mL Using the given table which of the following is the most restrictive level of significance or hypothesis test that would indicate the company is packaging less than the required average 300 mL a Critical z values O 1 O 2 5 5 O 10 Upper Tail Values 5 1 65 2 5 1 96 1 2 58

Find the coordinate vector of p relative to the basis S P P2 P3 for P2 p 5 7x 4x P 1 P x P3 x P s i

How is the value 5 calculated b In the diagram below iii Find the gradient of the line Write the equation of the line in the form y mx b Find the exact value of y when x is 6 Explain your methods clearly y R

Match the expression to the appropriate property Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE Fork 0 xl k means that Fork 0 x k means that If x is a real number X D If a b For modd xm m Form even xm en m III E III III E E x korx k III is equal to xl is equal to x the equation has no solution E is equal to x then ab but is not always an equivalent equation

1 Complete the chart Parent Function Sketch Intervals of Increase Intervals of Decrease Symmetry End Behaviours 5 marks f x 1X f x x

Write a function y f x for simple harmonic motion whose graph has a maximum at 5 and next consecutive minimum at 4 3 Select one O a y 5 9cos 3 O b y 0 5 4 5 sin 3 O c y 4 9cos 3 O d y 0 5 4 5sin t NI

Select the correct choice below and fill in any answer boxes in your choice A The solution set is 00 14 U 2 00 Simplify your answer Type your answer in interval notation OB There is no solution Choose the correct graph of the solution set OA 20 16 12 OB 20 OD 20 16 16 12 12 8 4

Write an equation for the function graphed below 7 6 5 y 2 a

study investigated the job satisfaction of teachers allowed to choose supplementary curriculum for their classes vers eachers who were assigned all curricular resources for use in their classes The authors of the study wanted to know The two groups of teachers had different levels of job satisfaction They will use a significance level of 5 for their test a Critical z values Upper Tail Values 5 1 65 2 5 1 96 1 2 58 What is are the critical value s for z in this study O 1 65 and 1 65

Exer se o If the revenue function of a good has the following shape draw the marginal revenue 240 220 200 100 160 140 120 100 80 60 40 20 11 12 13

Draw and label all sides of a triangle that would have the following sine value sin x 1 Label angle x also 4 marks A C 0 B b a C