Quadratic equations Questions and Answers

An antenna is put on a steep roof of a house The angle of inclination of the roof is a 40 A wire is to be attached to the top of the antenna and to the roof The distance from the bottom of the antenna to where the guy wire is attached is L 18 ft feet the red distance The angle formed by the wire and the roof is B 27 NOTE The picture is NOT drawn to scale Find the length of the wire required length of wire ft Enter your answer as a number your answer should be accurate to 2 decimal places And how tall is the antenna

following cubic X 3 2 1 0 1 2 3 y 22 6 2 4 6 2 14 Find the equation of the function of the specified type that is the best fit for the giver y x

Consider the following quadratic X y 3 4 5 8 1 7 5 3 2 1 0 2 3 4 18 Find the equation of the function of the specified type that is the best fit for the giv y x 5 5 Plot the data and the equation

y x linear 2 1 0 1 2 3 3 7 4 11 Find the equation of the function of the specified type that is the best fit for the given data X 2 1 Plot the data and the equation y 20 10 y 13 9 5 1 10 20 2 3 4 2 1 10 10 20 20 y 1 3

Bella s score on a spelling test is a function of the number of hours she studies Which expression represents Bella s score on a spelling test if she studies for 3 hours OA 3 score B Score 3 C Score 3 D 3 score

2 Use a graphing calculator to find a linear model for the set of data Use x years since 1980 a Write the equation for broccoli b Write the equation for cucumber c In what year will the two quantities be equal Give a reason for your answer Year Broccoli Ib person Cucumbers Obinerren Annual U S Consumption of Vegetables 1980 1985 1990 1995 1998 1999 2000 1 5 2 6 3 4 4 3 51 6 5 6 1 3 9 b 4 7 5 6 65 6 8 6 4

The function f is defined as follows f x 3 x if x 0 x if x 0 a Find the domain of the function b Locate any intercepts c Graph the function d Based on the graph find the range a The domain of the function f is Type your answer in interval notation b Locate any intercepts Select the correct choice below and if necessary fill in the answer box to complete y O A The intercept s is are n D Type an ordered pair Use a comma to separate answers as needed There are no intercepts

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

a Use a graphing utility to graph f x 0 2x4 0 3x 0 9x 4 on the interval 3 2 and approximate any local maxima and local minima b Determine where f is increasing and where it is decreasing Q Use MAXIMUM to find the local maximum of the graph The local maximum occurs at x and has a value of y Round to two decimal places Use MINIMUM to find the local minima of the graph The local minima occur at x and at X and have values of y Round to two decimal places Use the smaller x value as x and y N

Answer the questions about the following function f x 4x x 3 a Is the point 2 11 on the graph of f b If x 1 what is f x What point is on the graph of f c If f x 3 what is x What point s are on the graph of f d What is the domain of f e List the x intercept s if any of the graph of f f List the y intercept if there is one of the graph of f

Click here to watch the video The angle of elevation from a point on the ground to the top of a pyramid is 25 20 The angle of elevation from a point 106 feet farther back to the top of the pyramid is 17 50 Find the height of the pyramid What is the height of the pyramid Round to the nearest integer ft Show Transcribed Text Find h as indicated in the figure n J BIZON 390 17 50 25 20 106 h h

6 On hypotenuse AB of right triangle ABC draw square ABLH externally If AC 6m and BC 8m find CH H 10 A 6 B CO

Take k9x109 N m C A charge Q is distributed uniformly on the surface of a spherical conducting shell of radius 10 cm The magnitude of electic field on the surface is 10 V m What is the magnitude of electric field 20 cm from the center of the shell 45x10 V m 25x103 v 771 450x10 V m 500x10 V m K

Central Angles Pre Test Active 1 2 FH is tangent to circle G at point F 35 LL r 25 F 5 6 G 7 8 9 10 What is the length of the radius 10 units 12 units 20 units 24 units

1 2 In circle N KL ML 5x 24 3 K 7x 7 N 5 13x 2 L 6 M 8x 3 7 8 9 10 What is the measure of ZJNK 66 74 77 80

entral Angles e Test Active E 3 55 D 70 G 110 4 H 5 7 8 9 10 Which arc is congruent to EH GH OFH GE FG

Active 3 8 4 9 Y 5 Z 6 7 8 9 10 TIME RE 16 What must be the length of ZY in order for ZY to be tangent to circle X at point Y 14 units 15 units 16 units 17 units

Central Angles Pre Test Active 1 2 LL 3 4 In circle D ZEDHZEDG E 57 4 D F D 66 G 5 H 6 7 9 10 What is the measure of EH O 114 123 228 246

In circle A 2BAE ZDAE E X 10 3x 24 A A B D What is the value of x 14 O 17 27 34

For the following set of data find the number of data within 2 population standard deviations of the mean 63 62 95 33 65 62 57 Copy Values for Calculator Open Statistics Calculator

3 The population of Cool CA has been found to be able to be approximated by the function P t 464 603e0 045t for t 0 where t is in years and t 0 corresponds to the year 1980 W in what year will the population be 35 000

The graph has a vertical asymptote at x 3 a horizontal asymptote at y 0 and passes through the point 4 2 What could be the function of this graph 10 B 642 8 6 4 2 2 4 6 48 2 4 6 8 10

The graph has a vertical asymptote at 4 a horizontal asymptote at y 0 and passes through the point 3 4 What could be the function of this graph 10 8 6 4 10 8 6 4 2 co 2 12 4 6 8 10 2 lo

Consider the graph of the function f x log x Y 2 1 2 1 0 2 1 2 f 3 4 in 5 X Which are features of function gif g x 4 log x 4

me Left 1 11 06 Juelz James Which of the following is the graph of y a x 2 x x 1 where a 0

S S Solve the following system of inequalities graphically on the set of axes below State the coordinates of a point in the solution set y x 4 10 9 8 7 6 5 4 Change line 33 y 3x8 2 1 c 10 6 ch 9 8 N 10 10 4 3 2 7 2 H y Change shade 2 3 4 5 6 7 8 00 9 10 x

2 4 Use the graph to determine a the average rate of change between x 2 and x 6 b the instantaneous rate of change at x 4 4 3 2 A 56 8 9 10

Let f x 5x 7 For any 0 find the largest value of 8 such that if x 2 6 then f x 17 Expro cuorintormsofe

Trisha was given the graph of a logarithmic function 10 10 She identified the domain of the function as 4 0 Her answer is

5 L 3 2 1 2 3 4 5 12 F3 3 4 5 Match each transformation of function fto a feature of the transformed function function decreases as x increases asymptote of y 2 Hitone j x f x 2 h x f x 2 X g x 2f x y intercept at 0 2 y intercept at 0 4 S

Select the correct answer The table contains data on the number of people visiting a historical landmark over a period of one week Day Visitors B C 1 45 D 2 86 3 124 4 138 Which type of function best models the relationship between the day and the number of visitors 5 145 a linear function with a positive slope a quadratic function with a negative value of a a square root function a quadratic function with a positive value of a 6 158 7 162

If f x x which equation describes the graphed function A B C D 2 y f x 3 y f x 3 y f x 3 y f x 3 y 6 2 3 5

If the original exponential function defined by y 4 how would it change if y 2 4 2 3 1 where graphed instead

9 Graph each of the following a y sec x 2 2x 3 b y cotx R 2 Z 2x

4 Using radian measure represent all possible solutions to each equation a 2cos x 3 b cot x 1

Solve the given initial value problem y y 26y 24y 0 y 0 3 y 0 26 y 0 208 v x II

10 For angle 0 in the first quadrant cos 0 5 13 sin 0 tan 0 Calculate the following CSC 0 sec 0

1 Decide if each of the following statements is sometimes true always true or never true If it is sometimes true give the values for x that make it true if it is always true or never true explain how you know b sin x 2 2 a cos x 1 2

Solve each of the following equations a 3x 2 81 b 8 105

3 Solve each of the following equations in the domain 0 x 360 a csc x sin x b cot x 0 6

5 Find the vertex of the parabola given by the quadratic equation y 3x 12x 5

Enter the correct answer in the box Facundo crochets and sells baby blankets b Each blanket requires 3 skeins of yarn and the total number of skeins Facundo uses y varies directly as the number of blankets he crochets b Write an equation that models this relationship 0 10 of sin COC tani 1

Find the value of 2 Explain four to five different approaches including illustration to get the solution

X s 0 K 2 K 0 K S 1 s 25 65 4 3

The total cost in dollars to produce bins of cat food is given by C 18x 24160 The revenue in dollars is R 2x 480x Find the profit Recall that profit is revenue minus cost P At what quantity is the smallest break even point In other words how many bins of cat food must be produced and sold to make the profit equal to zero

10 16 3 in 10 3 2 1 A The graph above shows the function f x The graph below shows g x m 3 N 4 2 3 4 5 6 N 2 3 4 5 6 g x is a transformation of f x where g x Af Bx where

X X Two Solutions y x 2x 3 x 2x 3 0 2 2 4 1 3 2 1 2 16 2 2 6 2 2 214 2 1 3 Positive number in the discriminant b 4ac0 Two distinct real number solutions Can also factor x 1 x 3 0 y x 2x 3 intercents One Solution Associated Graphs One repeated x intercept No Solutions No x intercepts

2 If f x 3x 5x 7 find 2 O 15 O O O 7 05

1 Use the table below to find a prediction equation to show how altitude in thousands of feet relates to rainfall in inches Altitude Rainfall Oy x 3 y 3x 1 O y 2x 1 Oy x 3 0 2 5 12

Sketch a graph of x 1 8 7 Clear All Draw 465 I 6 5 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8 3 2 1 2 2 3 4 5 6 7 00 3 4 5 8 Question Help Video 6