Quadratic equations Questions and Answers

Find the LCD for each set of rational expressions and 2x 16

Combine the rational expression into a single fraction and reduce it in lowest terms X x 2x 24 11 x 3x 28

x x 3 3 x 3

x x 9 3x 27 x 1

1 x 3x 4 1 x2 2x 8

2 x 9 x 3

1 Itz

2x 7x 4 x 10x 24

Amy has purchased a basic letterpress kit for 140 She plans to make wedding invitations She estimates that the cost of the paper and envelope for each invitation is 2 Model this situation with a rational function that gives the average cost of a wedding invitation when the cost of the kit is included in the calculation Use the graph of the function to determine the minimum number of invitations that brings the average cost below 5 2w 140 W Given C w represents the average cost in dollars of a wedding invitation when the cost of the kit is included graph it using key features Then select two choices that are true about the function C w A There is a zero at 2 B There is an asymptote at x 0 C There is an asymptote at y 2 D There is a y intercept at 2 Average cost dollars 876543N 0 c W 20 40 60 80 Number of invitations A zero implies an x intercept

35 n 4n 4 2n 2 2 1 8n 5 4 3 2 1 0 1 3 4 5 36 4 6 4n 6n 4n 2 8 4n 7 6 5 4 2 1 0 2 3

31 8 6a 3 2 26 2a 7 6 4 3 2 1 0 1 2 3 32 5 7b s 6 46 6 H 1 0 1 2 3 4 5 6 7 8

27 4 6n 4 n 1 11 2 1 0 1 2 5 6 7 8 28 16 8x 7x 2 8x 4 3 2 1 0 1 2 3

21 13 1 2x 10 8 6 22 9 8 x 153 2 5 6 7 10 11 12

14 98x 32x 0

Simplify the following expressions x 1 1 x

6 9x 5x 9 6x 7x 5x 9

7 3x 2 2x 5 x 8

2 12x 8x 3x

17 x x 56

16 x 27 0

1 f x 14

10 Find the zeros y x x 2 x 5

15 4x4 1 0

13 3x 24 0

4x 6x 9 9 9x 8x 7x 3

2 f x 19 13x 6x 2x

9 5x 6 x 4x 3

6 9x 5x 9 6x 7x 5x 9

rite 5x 25 as an equivalent expression with a denominator of x 5 x 1

Simplify the expression Then write the expression as an equivalent expression with a denominator of x

Find the LCD for each set of rational expressions x 6 and 8x 24 14x 10x 30

e the rational functions below to answer the following questions f x 2x 4x x 4 State the point of discontinuity i e hole of the function x Identify the x intercept of the function Find the vertical asymptotes if any of the function

Select which statement of the following rational functions given is true f x 3x 6 x 3 A The graph has no asymptotes B The graph has a vertical asymptote at x 2 C The graph has a horizontal asymptote at y 3

Find the rational function s asymptotic x intercepts and holes Also sketch the graph of the rational function Then list the domain and range using interval notation f x x 2 x 2x 3 19 7 ge 7 0

Find the rational function s asymptotes x intercepts and holes Also sketch the graph of the rational function Then list the domain and range using interval notation f x x 1 x 3x 4 on sa 7 7 7 0 5

To test if the graph lies above or below the x axis create a number line with intervals Then choose test values before in between and after the intervals to determine if the function is positive or negative in that area A positive value means the graph is above the axis and a negative value means the graph is below the axis Try This Practice testing values to determine if the values are above or below the axis Circle if the graph of f x would be positive or negative in areas A B C and D Area D is done for you below A B C f x x 2 x 1 x 3 x axis Area A Area B Area C Area D 2 x 10 f 10 Match the appropriate test values for each area x 10 x 1 5 x 5 x 0 12 11 7 1 12 77 3 D x 2 Sign of f x x 1 x 3 positive

Graham wants to take snowboarding lessons at a nearby ski resort that charges 40 per week The resort also charges a one time equipment rental fee of 99 for uninterrupted enrollment in classes The resort requires that learners pay for three weeks of classes at a time The function f x represents the situation f x 40x 99 A There is a zero at 0 B There is an asymptote at y 40 DC There is an asymptote at x 0 D There is a vertical shift up 99 units X Select two choices that are true about the function f x

Rewrite the function in the form g x a using inequalities 4x 15 2x 6 a 1 k and graph it Also state the domain and range 5 3 5 4 2 3 3 2 1 2 1 0 1 N 3 4 5

Ex 6 3 x 1 7

Ex2 x 50

Ex 6 3 x 1 7

Ex 1 x 81

cs but no term term from ax2 bx c 1

Ex 5 2 x 4 32

Ex 3 3x 6 60

Rewrite the function in the form g x a 1 k Also state the domain and range using inequalities x h g x 4x 11 x 1

Amy has purchased a basic letterpress kit for 140 She plans to make wedding invitations She estimates hat the cost of the paper and envelope for each invitation is 2 Model this situation with a rational Function that gives the average cost of a wedding invitation when the cost of the kit is included in the calculation Use the graph of the function to determine the minimum number of invitations that brings the average cost below 5 2w 140 W Given C w represents the average cost in dollars of a wedding invitation when the cost of the kit is included graph it using key features Then select two choices that are true about the function C w A There is a zero at 2 B There is an asymptote at x 0 C There is an asymptote at y 2 D There is a y intercept at 2 Average cost dollars 5432768 0 C W 20 40 60 80 Number of invitations A zero implies an x intercept

Rewrite the function in the form g x ah k Also state the domain and range using inequalities 1 g x 4x 11 x 1

Identify the transformations of the graph of f x 1 x that produce the graph of the given function g x Then graph g x on the same coordinate plane as the graph of f x by applying the transformations on the asymptotic x 0 and y 0 to the reference points 1 1 and 1 1 Also state the domain and range of g x using inequalities g x 2 1 6 6 4 3 2 1 0 1 12 5

Rewrite the function in the form g x a inequalities g x 3x 8 x 2 k and graph it Also state the domain and range using 6 4 2 6 2 2 y 2 4 6 x