Quadratic equations Questions and Answers

3x 2 5 5 2

9 54x y x 3 12 X

Gx x y 5 2x y 4x8y

13x5 7 12 6 br

6 16 x y 6 Ne fo taxt XESCH SE Im

Find a polynomial function f x of least degree having only real coefficients and zeros as given Assume multiplicity 1 unless otherwise stated zero of 3 multiplicity 2 and zero 5i f x Simplify your answer

Given that 2 is a zero of the polynomial function f x find the remaining zeros f x x 10x 41x 50 List the remaining zeros other than 2 Simplify your answer Type an exact answer using radicals and i as needed Use a

For the polynomial function a list all possible rational zeros b find all rational zeros and c factor f x f x x 2x 13x 10 a Determine the possible rational zeros for f x Choose the correct answer below OA 1 2 5 OC 1 2 5 b Determine the rational zeros for f x Choose the correct answer below A 1 2 5 O C 1 OB 1 2 5 10 D 1 2 5 10 OB 1 2 5 10 OD 1 2 5 c The factored form of f x x3 2x 13x 10 is f x Simplify your answer Factor completely Use integers or fractions for any numbers in the expression

Estimate the x and y intercepts from the graph x intercept s 14 y intercept s 2 34 2 Write each intercept as an ordered pair Separate your answers using commas if necessary Select None if applicable 13 0 0 None 0 0

Let f t 5et For what value of t will f t 10 Round to 2 decimal places t

The graph of the polynomial f x is given below If f z has degree 4 find the factored equation for f x Provide your answer below f x 2

The graph of the polynomial f z is given below If f x has degree 3 find the factored equation for f x f x 2 3 2 1 1 2 3 0 3

1 a Use the fundamental theorem of algebra to determine the number of roots for 2x 4x 7 b What are the roots of 2x 4x 7 Show your work Answer

sin r cos r OO None of above

a Graph the function b What are the x and y intercepts of the graph Answer 6 5 4 3 2 1 6 5 4 3 2 1 1 y 2 3 4 5 1 2 3 4 5 6

Score for Question 3 of 6 points 3 Simplify the expression x3 5x2 7x 12 x 4 using long division Show your work Answer

3 C4x ry 2

2 718x 35

Evaluate

23 Evaluate 16 25

T2 5 25 Evaluate 42 2 45 1 2 5 2 32 26

24 Evaluate 85 3 8 2

13 Write 80 in simplest form Brue 31

7 Determine if the following numbers are rational or irrational a 41 b 7 2 irrational Rational because itisa Fraction e 121 2 d 77 irrational irrational Rational

14 Write 54 in simplest form 3 271 0 22

11 Write 108 in simplest form 54 2

10 Write 32 in simplest form 1612 1 2

9 Write 12 in simplest form 6 2

6 Evaluate 27 m 00 5

The table shows ordered pairs for a polynomial function f X 2 1 0 1 2 3 4 What is the degree of f Enter your answer in the box f x 30 0 2 0 30 160 510

X 3 a 3x 4 6x 4x 16x 2 X 3 3 3 3 6 4 16 2 E 3 36 4 16 2 3

Is the binomial a factor of the polynomial function f x x 2x 16x 32 Select Yes or No for each binomial x 2 x 2 x 4 x 4 x 6 Yes O O O No O

Which statements are true about the polynomial function x x 5x 6x Select each correct answer x 2 is a factor of f x O f 2 0 Of x 0 when x 2 f x divided by x 2 has a remainder of 0

One of the zeros of the polynomial function is 5 f x x 4x 21x 100x 100 What is the factored form of the function O f x x 5 x 5 x 2 f x x 2 x 5 Of x x 2 x 2 x 5 O f x x 5 x 5 x 2 x 2

What are the zeros of the polynomial function f x x 2 103z 200z 300 Select each correct answer 0 10 0 3 0 1 00 0 3

Divide 4x 2x 1 x 1 4x 4x 6 711 O 4x 4x 6 O 4x 4x 6 O 4x 4x 6 5 5 x 1 5 x 1 5 x 1

What are the factors of the polynomial function Use the rational root theorem to determine the factors f x x 6x 3x 10 Drag each factor of f x into the box Factors of f x

3 3 4 5 6 7 8 9 Mrs Smith wrote Eight less than three times a number is greater than fifteen on the board If x represents the number which inequality is a correct translation of this statement a 3x 8 15 b 3r 8 15 O O a b C c 8 3x 15 d 8 3x 15 4

B 1 Verify Solutions Linear Inequality Determine which point or points are solutions of each linear inequality gfiven 2 3x 5y 10 1 x y 3 46 5 3 y 2 5 Ay y 6 x X 2 4 6 5 4 3 2 4 5x 2y 10 4 3 2 1 4 Y AV 6 x 4 X

16 The cheerleaders are selling tickets to the spaghetti dinner They need to raise at least 900 The tickets cost 5 each Write an inequality to represent how many tickets they need to sell to meet their goal use t for the number of tickets sold Type a response

13 Julie is taking a taxi cab to a restaurant in the city The cab charges 3 20 plus 55 per quarter mile Julie only has 15 to spend on the cab Write an inequality to represent the how far away the restaurant can be so that Julie can afford the taxi fare Use m for the number of quarter miles Type a response

14 Sam has saved 250 from working this summer Hel keeps saving at a rate of 20 per week After how many weeks will he have more than 500 Write an inequality to represent this situation use w for the number of weeks Type a response

Translate the verbal phrase into an inequality use x as your variable Don t solve The sum of x and 1 is at least 9 Type a response

Suppose that you want to estimate the effect of years of education on log wages using those variables and some other explanatory variables You consider estimating by OLS a Explain the conditions needed for obtaining a consistent estimator by OLS bj Give a proof that OLS is consistent for the case of one explanatory variable Explain the role of assumption MLR 4 c Explain what happends to the consistency result if you exclude a relevant explanatory variable

Find all real solutions of 25x 1 3 10z If there are no real solutions or t solution is all real numbers briefly EXPLAIN how you know that is the case

A regulation size pool table is 9 feet long by 4 5 feet wide Treasure is standing at the lower left wants to hit the white ball so it will bounce off the top cushion and hit the red ball directly in the center From physics she knows that the angle 0 the ball hits the cushion is the same as the angle 02 that it comes off the cushion How far from the top left corner should she aim the white ball The positions of the balls are shown below in feet 1 6 1 1 1 0 0 2 7 2 3 Hint Draw some triangles and try to find a suitable unknown x that you can use to describe the sides of the triangles in terms of the angles Then use 0 0

7 Write the functions below as compositions of two or more non identical functions f x cos 4x f x 1 2x 4 2x 2x

Graph the function g x 2 x 2 x 6 9 8 7 6 5 4 3 2 17 You might need Calculator Y 6 8 7 6 5 4 3 2 1 2 3 x 1 2 3 4 5 6 7 8 9

Graph the equation 3 y x 3 x 7 4 9 8 7 6 5 4 3 2 8 7 6 5 4 30 6 2 14 21 2 23 Y 3 H 11 1 2 3 4 5 6 7 8 9 x

C u 10 Given the vector space V spanning set of V A 8 B 5 span 7 1 2 8 1 1 Find x R such that M 48 6 6 2 4 x is a C 7 D 6