Quadratic equations Questions and Answers

Let y f a be the piecewise defined function given below a f 2 b f 1 c For what values of r is f x 0 help numbers Domain Range help numbers help inequalities x 1 d Find the domain and range of f You may find it helpful to graph this function on your own paper to find the domain and range Your answers must be inequalities not intervals help inequalities help inequalities f x 0 x 1 if a 1 if 1 x 1 if a 1

The weight y of a fiddler crab is directly proportional to the 1 25 power of the weight x of its claws A crab with a body weight of 1 8 grams has claws weighing 1 1 grams Estimate the weight of fiddler crab with claws weighing 0 85 gram The crab weighs approximately grams Type an integer or decimal rounded to the nearest hundredth as needed

Use a calculator to solve the equation on the interval 0 0 2n cos 0 0 52 IXE What are the solutions in the interval 0 0 2n Select the correct choice and fill in any answer boxes in choice below A The solution set is Type your answer in radians Round to two decimal places as needed Use a comma to separate answers as needed OB There is no solution

A pole 5 feet tall is used to support a guy wire for a tower which runs from the tower to a metal stake in the ground After placing the pole Camden measures the distance from the pole to the stake and from the pole to the tower as shown in the diagram below Find the length of the guy wire to the nearest foot t to scale 19 ft 5 ft 12 ft Oct 8 3 40 US 9

Part 1 of 4 Use the vertex and intercepts to sketch the graph of the quadratic function Give the equation for the parabola s axis of symmetry Use the parabola to identify the function s domain and range f x 4 x 1 2 Use the graphing tool to graph the equation Use the vertex and the y intercept when drawing the graph Click to enlarge graph CIE Ay 20 12 Q

Given f x 2x 4x 8 answer the following questions Vertex Axis of Symmetry Y Intercept Minimum Type your answer as a coordinate point without spaces Type your answer as an equation without spaces Type your answer as a coordinate point without spaces GRAPH THE QUADRATIC IN YOUR NOTEBOOK

Factor the expression completely 7x 7x 84 7x 7x 84

Solve the quadratic equation by factoring 7x 8 1 Write your answer as an integer or an improper fraction X X

Factor f x 2x 92 5 f x b Type your factors without spaces

Solve 2 2x x 21x The solution set is Type your answer in interval notatic

Prove the fencity lept CSC X sin 2x Note that each Statement must be based on a Rule chosen from the Rule menu To see a detailed description of a Rule select the More Information Button the right of the Rule Statement RE Im Tue Select Rule 0 0 DID 0 0 0 0 D B D D 0 0 D D

Factor by grouping sometimes called the ac method 10x x 2 First choose a form with appropriate signs Then fill in the blanks with numbers to be used for grouping Finally show the factorization Form O O 10x 2 0 O 10 2 0 0 2 10x O 0 0 10x Factorization 10x x 2 X S

Solve the initial value problem y 3y 4y 0 y 0 1 y 0 11 The general solution is y x www

Baby Zia has 10 less than 9 times as many toys as Baby Zion Together Baby Zia and Baby Zion have 180 toys How many toys does Baby Zia have

Post a short discussion on Double Angle Half Angle and Reduction Formulas at least 50 words minimum and in your own words and not copying from a website or your textbook

Use the graphs of the functions to solve the problem f x x 3 g x 6 a f x g x b f x g x c f x g x 12 Tex 6 to co 6 12 compound inequality O D The solution set is the empty set c Solve f x g x Select the correct choice below and if necessary fill in the answer box to complete your answer OA The solution set is x Simplify your answer Type a compound inequality OB The solution set is Simplify your answer Use a comma to separate answers as needed OC The solution set is x x or x Simplify your answer Type inequalities OD The solution set is the empty set

Determine the extreme values for each function on the interval 3 x 4 and include if any extreme values found are maximum or minimum values 10 f x 3 12 f x 3x 8

Score 0 37 0 11 answered Question 6 1 2 a 2 a 1 a Solve the following equation Be sure to check each answer in the original equation if you multiply both sides by an expression that contains a variable V 2 a 3a 2 Question Help Video Post to forum

Score 0 37 0 11 answered Question 1 Choose the correct words to fill in the blanks below multiply denominators least common denominator 1 The first step to solving a rational equation is to find the in the equation 2 The second step to solving a rational equation is to by the LCD 3 Multiplying a rational equation by the LCD clears the equation of all 4 If we get a then we write the equation in standard form factor and solve Question Help Post to forum quadratic for all denominators both sides of the equation equation once we have multiplied a rational equation by the LCD

3 2 Score 0 14 0 7 answered Question 3 I For the following exercise solve the radical equation Be sure to check all solutions to eliminate extraneous solutions x 7 2 Question Help VIDEO OPost to forum

Which graph represents f x 2x O 6 5 4 3 2 151 6543 2 1 IN 1 2 3 1 2 3 4 5 X 6 O 5 4 3 2 6 5 4 3 2 1 2 3 2 PN 3 4 5 6 X

A D 1 F x 3x 1 ii G x x 1 iii H x x 1 iv I x x 1 B C

Here are four graphs Match each graph with a quadratic equal Column A 1 2 T N O 2 2 Column B a b C d y x 3 y x 1 x 3 y x 1 x 3 y x 3

Which equation is represented by the graph yf 10 O a O b Oc Od 3 1 y x 1 3 2 y x 3 1 y x 3 1 r 3 2 11 6 X

1 Find the slope of each line GIVEN a graph or an equation 2 1 2

1 3 SUM Find the slope of each line GIVEN a graph or an equation 2 1 3 8 2y x 4 2 4 y 2x 2 0

Find the real solutions of the equation 3 5t 3 21 Select the correct choice below and fill in any answer boxes within your choice O A The solution set is OB The solution set is all real numbers OC The solution set is the empty set Use a comma to separate answers as needed

Solve the absolute value inequality Graph the solution set 2 3x 5 The inequality 12 3x 5 is equivalent to 2 3x or 2 3x Select the correct choice below and if necessary fill in the answer box to complete your choice O A The solution set in interval notation is Type your answer in interval notation Use integers or fractions for any numbers in the expression OB The solution is the empty set Graph the solution set Choose the correct answer below O A 4 2 0 2 4 6 8 O B 2 0 N 2 st 6

Use the FOIL method to find the product 3x 8 5x 1 3x 8 5x 1 Simplify your answer

w4 12 W W4 12 W 11 Use positive exponents only

Find the special product x 12 x 12 2 Simplify your answer

Evaluate the expression 13 3 2 13 3 22

4x7 7x 4x 7x Oman16 intogoro or fractions for any numbers in the

Simplify the expression xy 4xy5 x y 5 4xy 5 Simplify your answer

Solve the equation Check your solution 2p 6 12

Solve the equation Check your solution 8z 11 7z 6 The solution set is Simplify your answer

8 i 3 3i 8 i 3 3i Simplify your answer Type your answer in the form a bi

Domain 4 4 Range 4 4 Function NO Domain 0 0 Range 4 Function YES Domain 0 00 Range 0 0 Function NO 7 Domain 7 5 Range 3 1 Function YES D 10 G Domain 3 51 Range 1 Function YES Domain 6 6 Range 0 6 Function YES 8 Domain 3 4 Range 2 4 Function NO 11 Domain 00 00 Range 0 00 MA Function VES B 11 Domain 4 2 Range 2 4 Function YES Domain 5 6 Range 2 6 Function NO Function YES 9 Domain 0 00 Range 00 00 12 R ARE Domain 3 4 Range 0 5

Directions Fill in the table The first one is done for you as an example Example 31 10 Frot 204 30 X 4 3 1 0 1 2 3 4 Y 1 0 2 3 2 1 0 1 Value of the zero s 4 Answer based on the continuous function that is given in this table 3 0 2 Value of the y intercept s 0 Identify the interval s where the function is negative Identify the interval s whe the function is positive

Multiply x 4 x 3x 5 Ox 5x 5x 20 Ox 2x 8x 20 Ox x 7X 20 Ox 7x 17x 20

Simplify the expression 4 x 5 x X 2 O 4x 4x2 3x 10 O4x 16x 12x 40 ww O 4x 12x2 40x 40 O 4x 40x 12x fm

4 2x 5 20 X X

2x 63 11 X X

5x 50 X X

A square matrix B b mxm is said to be a diagonal matrix if all its non diagonal elements are zero that is a matrix B b mxm is said to be a diagonal matrix if b 0 when i j For example A 4 B of order 1 2 3 respectively v Scalar matrix For example A diagonal matrix is said to be a scalar matrix if its diagonal elements a that is a square matrix B b x is said to be a scalar matrix when i j when i j for some constant k A 3 B 1 1 C 0 b 0 ij b k C 0 coffe 0 are scalar matrices of order 1 2 and 3 respectively identity matrix if a kira of For example 1 3 0 1 1 O 0 0 20 0 03 vi Identity matrix A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an identity matrix In other words the square matrix A a x is an 1 if i j if i j 1 are diagonal matrices We denote the identity matrix of order n by I When order is clear from the context we simply write it as I 1 00 0 1 0 00 1 e equal are identity matrices of order 1 2 and 3 Rationalised 2023 24 respectively Observe that a scalar matrix is an identity matrix when k 1 But every identity matrix is clearly a scalar matrix 0 0 For example 0 0 0 zero matrix by O Its order will be clear from the context MATRICES vii Zero matrix A matrix is said to be zero matrix or null matrix if all its elements are zero 3 3 1 Equality of matrices Definition 2 Two matrices A a and B b are said to be equal if i they are of the same order 41 0 0 are all zero matrices We denote ii each element of A is equal to the corresponding element of B that is a b for all i and j

Definition 2 Two matrices A a and B b are said to be equal if i they are of the same order ii each element of A is equal to the corresponding element of B that is a all i and j 3 For example 2 and 2 1 not equal matrices Symbolically if two matrices A and B are equal we write A B X y 1 5 0 If z a 2 b C 3 Example 4 If x 3 42 Simplifying we get 6 then 2 6 a 1 b 3 21 z 4 2y 7 MATHEMATICS 0 2 are equal matrices but Free 5 Find the values of a b c x y and z Solution As the given matrices are equal therefore their corresponding elements must be equal Comparing the corresponding elements we get x 3 0 z 4 6 2y 7 3y 2 a 1 3 b 3 2b 4 Solving these equations we get 1 In the matrix A 35 2 0 2c 2 a 2 b 7 c 1 x 3 y 5 z 2 Example 5 Find the values of a b c and d from the following equation 2a b a 2b 4 3 H 5c d 4c 3d 24 6 2b 4 21 0 6 3y 2 3 2c 2 Rationalised 2023 24 a 1 b 2 c 3 and d 4 19 5 Solution By equality of two matrices equating the corresponding elements we get 5c d 11 2a b 4 a 2b 3 4c 3d 24 EXERCISE 3 1 12 3 2 1 a 6 b 3 c 2 17 and write b for 3 1 5 i The order of the matrix ii The number of ele iii Write the elements a13 a21 9332 A242 23 2 If a matrix has 24 elements what are the possible has 13 elements are ned it can have What if it 3 If a matrix has 18 elements what are the possible orders it can have What if it hata

1 y 3 x 1 2 a Graph the function by hand b Identify the vertex c Label at least one point on either side of the vertex d Take a picture of your graph and upload 2 Write a quadratic function in vertex form similar to 1 to model the graph G ve a reason for your answe 4 2 2 0 2

Belle and her friends are planning a weekend trip to Isle of Palms South Carolina They can rent either a sedan or a fuel efficient SUV for the trip The sedan will cost 180 to rent while the SUV will cost 200 Belle estimates that the sedan will cost 0 11 per mile in fuel while the SUV will cost about 0 06 per mile How many miles would Belle and her friends need to drive for the total cost of the vehicles to be the same Simplify any fractions

The graph below represents the equation y x 3 1 ty 4 Select one O True O False Check 2 2 2 O 2 2 Select one O True 0 The graph below represents the equation y 2 x 1 3 2 X

Describe the translation from the parent function y x y x 2 Choose y x 2 y x 2 y x 2 y 2x Check Identify the v y 2 x 1 Answer Choose Choose Choose Choose Choose translated 2 units to the right translated 2 units down translated 2 units up translated 2 units to the left stretch by a factor of 2 47 ED