Quadratic equations Questions and Answers

What is the exact solution to the equation 2 2 52 2 O 2 In 2 O 2 In 5 In 2 O In 2 2 ln 5 In 2 O 2 In 2 2 ln 5 In 2 In 2 2 In 5 In 2

1 6 Discuss the continuity of the function fat x 0 Iff is discontinuous at x 0 is it removable Sketch f 14 13 I 0 f x 1 x 2 1 x if x 0 if x 0 if x 0 3 steps

Fill in each blank with the appropriate word add subtract multiply or divide number or expression Recall that the solution set is denoted with curly braces a To solve the equation 2x 14 we must Write your response here Type your answer here Write your response here The solution is X Type your answer here b To solve the equation x 2 14 we must Write your response here Write your response here side of the equation The solution is X Type your answer here each side of the equation by 677 and the solution set is Type your answer here and the solution set is to each

Choose the correct description for graphing the solution set of the inequality X 5 Select an answer and submit For keyboard navigation use the up down arrow keys to select an a Q3 Graph inequality Homework Answered Due Jan 16th 11 59 PM b C d Shade to the left of 5 and put a bracket on 5 Shade to the right of 5 and put a bracket on 5 Shade to the left of 5 and put a parenthesis on 5 Shade to the right of 5 and put a parenthesis on 5

10 4x 10x x x 4

15 Lety ax 4x 5 a Find the vertex algebraically using the formula d Write y x 4x 5 in vertex form c Graphy x 4x 5 by plotting the points you found above b Find the zeros x intercepts algebraically by factoring e Write y x 4x 5 in factored form intercept form 16 a Write y x 1 x 7 in standard form 18 a Write y 3 x 2 3 in standard form b Find the vertex 17 Write y 2x 4x in vertex form hint find the vertex first then remember to use the a b Now write it in factored form

8 36x 49 0

14 y 2x 4x

12 5w 30w

4 y 8x 18x 9

7 x x 20 C

5 y 4x 12x 8

3 x 16

6 y 3x 8x 5

1 x x 2

Zoe is a high school basketball player In a particular game she made some free throws worth one point each and some two point shots Zoe made a total of 11 shots altogether and scored a total of 15 points Write a system of equations that could be used to determine the number free throws Zoe made and the number of two point shots she made Define the variables that you use to write the system Answer Attempt 1 out of 2 Let Let System of Equations

y 2 x 4 Move Line 10 9 8 7 6 5 4 3 2 10 TY 9 8 7 6 5 4 3 2 19 2 3 Undo 4 1 2 3 4 Redo 5 6 7 x Reset 8 00 9 10 X

3 Find all values of x that make the equation true extraneous solutions X 2x 1 3 Show y x 2

10 Which graph represents the solution of the system of inequalities Don t just choose an answer show work and explain x y 7 v 4x 2 A C 10 3 2 1 21 6 10 B 3 2 1 D

9 Answer the following questions and draw a rough sketch of the function f x x 8x 8x 96x 144 What is the general shape of the function Does the function open up or down What is the function s y intercept If one of the factors is x 6 how would you show that on the graph

20 Solve for x 3x 4x

15 Right triangle ABC has its right angle at C AC 9 and BC 12 Draw and label the triangle What are the following trigonometric ratios sinA COSA tanA

13 Solve for a e f c 2 22

12 Multiply and simplify 32x 8y 10x

1 Algebra Prep 2023 Kuta Software LLC All rights re served Radicals and Rational Exponents 2 Write each expression in radical form 4 1 x A 3x C 5x 3 3 6x A 6x C 4x B x D 5 A 7n B 3x D 7x Write each expression in exponential form 4 3n 3 B 3n 4 2 7 A 4x C x 5 5 b 2 A b B 3x D x WIN B b zoom in 3

18 As more people join streaming tv and movie services fewer people buy cable every month The function f x 0 82 0 91 models the number of cable subscribers in millions each month since this trend began Answer the following questions about the values in the function a How many subscribers were there when the trend began b How do you know c By what percent does the number of subscribers decrease each month d How do you know

The graphs of the functions f and g in the figure are obtained by vertical and horizontal shifts and scalings of y x Find formulas for f and g Verify your answers with a graphing utility y x X f x X x g x f x 4 x 51 Type an expression using x as the variable g x Type an expression using x as the variable N

2 In a recent alien autopsy scientists discovered a new radioisotope Xenos 6 The half life of this isotope is 6 weeks Write and explain an equation that determines the percent of an initial amount of the isotope remaining after t weeks

8 Solve for x 18x 1 3x

22 The length of a rectangle is 5 inches longer than its width The perimeter of the rectangle is 40 inches Write an equation in terms of width w that you can use to find the rectangle s length and width Now solve the equation What are the width and length of the rectangle

23 A rectangular crate of bottles holds 72 bottles The rows across the width of the crate hold 1 bottle less than the rows across the length of the crate Write an equation where b is the number of bottles in the longer rows that can be used to solve this problem Now solve the equation How many bottles are there in the longer rows

25 Graph the solution on the number line below 4 x 3 16

Solve by completing the square x 18x 93 O 18 231 18 231 O 7 i 6 7 i 6 O 9 2 3 9 2i 3 O 9 174 9 174

25 Graph the solution on the number line below 41x 3 16

What is the exact angle measure in radians 540

4 What are the roots of the polynomial f x x 2x 7 x 5

Which value must be added to both sides of the expression x 6x to make it a perfect square trinomial O 9 08 36 9

19 Write the following as a single logarithm 3logy logz 4logx

7 Simplify the radical expression a5b

3 Solve 2x 6 3 x

24 Solve 7 2x 51 21

20 Solve for x 3x 4x 3

17 Simplify x2 3x 2 X 4 2x2 x 3 x2 16

Write a rational equation for the real world application Then solve A glassblower can produce several sets of simple glasses in about 3 hours When the glassblower works with an apprentice the job takes about 2 hours Write an equation that can be used to find the amount of time t i hours it would take for the apprentice to make the same number of sets of glasses when working alone

ombine the rational expressions into a single fraction and reduce it in lowest terms 3x 1 x 2 x2 3x 18 x 6

Select two choices that are true about the function f x A There is an asymptote at x 0 B There is a zero at 23 C There is a zero at 0 D There is an asymptote at y 23 23x 14 x

3x 1 5x Find the quotient of the following 12x 6 10x 5x

Find the product of the following 2 14x 45 3x 2x 1 6x 3x 2x 50

Combine the rational expressions into a single fraction and reduce it in lowest terms 13x 10 3x 1

A Determine which of the following graphs is the graph of the given function x 1 f x 24x C 3 B D 6 4 T 2 0