Quadratic equations Questions and Answers

Find the equation of the quadratic function satisfying the given conditions Hint Determine values of a h and k that satisfy P x a x h 2 k Express the answer the form P x ax bx c Use a calculator to support the result Vertex 1 2 through 6 145 CIU The equation of the quadratic function satisfying the given conditions is P x 16x 32x 14 Simplify your answer

17 A Elm El dy dx sin x dx 3 2 3 B 2 3 3 D 2 3 2 3 2 E 3 2 2 C

1 point An open box is to be made out of a 12 inch by 16 inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides Find the dimensions of the resulting box that has the largest volume Dimensions of the bottom of the box Height of the box

2 Select the correct answer A low hedge is planted around a triangular fountain as shown What is the approximate length of the entire hedge A 170 7 feet B 236 6 feet C 111 8 feet D 220 7 feet

A rare square Turkish rug is sold at auction The area of the Turkish rug in square feet is 60 more than its perimeter in feet Find the length in feet of the side Each side of the rug is feet Type an integer or a fraction

An orange triangular warning sign by the side of the road has an area of 135 square inches The base of the sign is 3 inches longer than the altitude Find the measurements of the base an altitude The altitude is inches Type an integer or a fraction

The equation 4x 7x c 0 has a solution of C 1 11 What is the value of c What is the other solution to the equation 4

72a b 63ab 9ab 2 9ab 72a b 63ab 9ab 9ab Simplify your answer Use integers or fractions for any

Multiply 6x 7 x 2x 1 6x 7 x 2x 1 Type a polynomial

Next question Factor Remove the largest possible common factor Check your answer by multiplication 40x6 16x4 32x 40x6 16x4 32x 0

Add the polynomials as indicated x 7x 8 6x 4x 1 x x 3 x 7x 8 6x 4x 1 x x 3 Simplify your answer Do not factor

Multiply 6x 9x 7x 5 6x 9x 7x 5 Simplify your answer

Suppose f is a polynomial with the following values x 8 7 12 2 f x 70 3 13 5 A linear factor of f x is

4 Horizontal and vertical lines Write the equation of the line a OTW b 10 11 0 2 8 10 prizontal and vertical lines asymptotes The most basic definition of an asymptote is a function below draw the asym

Suppose f is a polynomial with the following values 8 7 12 2 f x 7 0 3 13 5 A linear factor of f x is

Complete parts a and b below a Write the inverse of f x 7x 3 b Do the values for f1 in the provided table fit the equation for f1 X O Yes No 0 1 2 3 4 f x 3 4 11 18 25 X 3 4 11 18 25 a The inverse of f x is f1 x Simplify your answer Use integers or fractions for any numbers in the expression b Do the values for f1 in the provided table fit the equation for f f 1 x 0 1 2 3 4

Select the correct answer below 0 O OOO 25 04 O L 24 O 24 7 25

Let f x b where b 1 Match each characteristic of the graph off to the correct response Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE Domain Range x intercept y intercept Increasing or decreasing Equation of Asymptote III III III III 0 00 None 0 1 1 0 Increasing Decreasing 0 0 X X X X

Click on the center of the graph of the function f x 4 6 C D TH

d An antique table increases in value according to the function v x 850 1 03 dollars where x is the number of years after 2000 How much is the table worth in 2016 Fill in the formula Label your answer and round it to two decimal places X v x

A AT is A Angle bisector G RAT 3x 45 XGAT 7x 5 Find GAT

b Use S P 1 r to find the future value of 2 000 invested for 6 years at 4 compounded annually Fi in the formula Label your answer and round it to two decimal places P 2000 r 4 0 04 t 6 S

Click on the center of the graph of the function f x A C D

4 h x 3 x 4 1 or 14 to 5 3 Ty 2 10 4 2 3 4 5 2 3 4 a X

Click on the center of the graph of the function f x 4 A C D

5 Horizontal and vertical lines asymptotes The most basic definition of an asymptote is a line that the graph of the function gets close to but doesn t cross For each function below draw the asymptote on the graph and write the equation of the asymptote f x 2 a b 0 4 y log 2 luate it

Type your answers in all of the blanks and submit X X Fill in each blank with the appropriate number a 80 2 b 8 Type your answer here Type your answer here

An island is 4 miles from the nearest point P on a straight shoreline A town is 11 miles down the shore from P T x Use integers or fractions for any numbers in the expression b What is the domain of T 4 Island 28 X d a If a person can row a boat at an average speed of 3 miles per hour and the same person can walk 4 miles per hour express the time T1 t takes to go from the island to town as a function of the distance x from P to where the person lands the boat Town 11 x OA Domain x10 x 11 OB Domain x10 x 11 OC Domain x10 x 11 OD Domain x10 x 11 c How long will it take to travel from the island to town if the person lands the boat 4 miles from P T 4 hours Round to two decimal places as needed d How long will it take if the person lands the boat 9 miles from P

4 Rain leases a houseboat for 61 per day The total cost C is a function of the number of days d she leases the houseboat The best algebraic equation for the above situation is Do not include a dollar sign in your answer C

Answer the questions for the graph below Note The highest value of the graph is 38 38 y 19 14 14 28 42 To enter a value like 2 type 2 pi To enter a value like x type pi x Do not type pix 56 What is the amplitude Number 70 84 98 112 126 140 154 X What is the period exactly Do not enter an approximate value The period is Number What is the equation Do not include approximate values See above how to enter TIP Click on the Preview icon after the box which looks like to check your formula

2 The graph is not drawn according to scale and represents the functions of f and g where 2 f x x 2x 4 g x x 1 DM Ly axis and AB Lx axis 4 y DM Ho A 4 k 22 2 Calculate the coordinates of D if OM 12 22 3 1 Write down the value of k 22 3 2 Determine the length of AB 22 4 1 B 2 22 1 Write x 2x 4 in the form y x p q and write down the coordinates of Q the turning point of f If A were any point x y on f and B on g such that AB 1 x axis determine in terms of x an expression for the vertical length AB 22 4 2 Hence calculate the minimum length of AB g X 4 4 1 2 2 1

The graph shown is a transformation the graph of y sinz The pointed indicated has coordinates 5x 4x 3x 2 E RS The equation of the graph shown is y 2x 30 4 Spe Enter a sine function

2 This exercise shows a transformation of y 10 5 y intercept y 10 5 y intercept x y 5 10 a Find a neeelkie formally for the h W b Give the coordinates of any x and y intercepts x intercept a Find a possible formula for the graph f x 5 b Give the coordinates of any x and y intercepts x intercept x y 10 c Find the equations for the vertical and horizontal asymptote

Graph the trigonometric function y 3 tan 3 x Start by drawing two consecutive asymptotes Between those asymptotes plot three points a point where the graph intersects the x axis a point to its left a a point to its right Finally click on the graph a function button I 12 2 11 0 1 12

5 Let m p be a relation defined by the table below 5 3 1 3 P m p b Evaluate m 1 1 5 c Solve m p 7 0 0 1 5 a Is m p even odd symmetric about y x or none of the above Make sure to list ALL types of symmetry shown 3 3 What he domain of m p Write the domain in set notation 5

X X 2 Fill in each blank with the appropriate value Let f x x 4 and g x x 4 a f 5 Type your answer here 4 b Substitute the value from part a into the function g g Type your answer here Type your answer here

2 h x x 2 1 Ty 4 7 8 5 4 3 2 2 10 5 2 S 4 ch 6 N 32 A 10 9 X

Find an equation of the line shown Your answer should be written in standard form 2x 5y 0 x y RowBox RowBox 2 5 PraditionalForn X

These garage doors on this old house are in the shape of a trapezoid Plans are bei made to make new doors The wood underneath this paint is rotting Given these lengths find the three angles A B and C Make certain to denote which angle you are answering Round to the tenth of a degree B 96in A 58 25 in 124 5in

The graph of a function f is given Match the interval to the inequality it solves 6 5 4 E 3 2 1 50 40 30 20 10 10 20 30 2 3 4 5 6

If cos 0 0 in quadrant IV find the exact value of c tan 0 4 a sin 0 b sin 0

a Graph the function f x ex on the window 5 5 by 10 30 b Find f 1 f 2 and f 2 rounded to three decimal places c What is the horizontal asymptote of the graph d What is the y intercept a Choose the correct graph below A G B b f 1 2 718 Round to three decimal places as needed f 2 Round to three decimal places as needed C

Three O None Four How many of the following functions have the graph below 3x 1 4 2x 1 r x 2 r x 3 r x 4 r x Two 10 x 4 2x2 x 4 4x 1 2 4 10 10

Complete the table for the given polynomial 4a a 3a 5a 9 Term 429 24 a 3a 5a Coefficient Degree

Evaluate 3 using a double angle indetity

The vector u is shown in red Drag the blue movable point to construct the vector 4u Provide your answer below 10 5 y 10 5 4u 10 X

Homework Unanswered Click on the graph of the solution set of the inequality a 6a 4 2 0 2 4 6 8 10 4 2 0 2 4 6 8

The function f r has table 3 3 x Y The function 1 3 1 4 T y 2 5 g x has table 3 1 2 5 4 2 4 4 5 1 52 5 2 Calculate f g 4 Write your answer as an integer that is a whole numbe

Click on the graph of the solution set of the inequality x 2 x 3 0 2 3 3

Solve the inequality and write the solution set using interval notation without any blank spaces 5 x x 1 0