Quadratic equations Questions and Answers

The size of a rat population at the bay area of a certain city grows at a rate of 7 monthly If there are 150 rats currently find how many rats rounded to the nearest whole should be expected in 12 months Use y 150 2 7 0 07t and let t be 12 months Y rats

Observe the graph and identify the following key features 1 Identify the intercepts 2 If n is odd or even 3 The number of turns 4 If constant a is positive or negative 5 The degree of the polynomial 17 JA 2 12345 1 2 5

Identify the transformations of the graph of f x 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 to the reference points 1 1 0 0 and 1 1 g x x 2 Reference Points 1 1 0 0 1 1 First Transformation Second Transformation 4 2 4 2 0 2 2 4

Which graph is sketched to the right A g x x 1 x 2 x 3 B g x x 1 x 2 x 3 C g x x 1 x 2 x 3 2 0 X

Given the function y x 2 Place a point on the coordinate grid to show the x intercept of the function Place a point on the coordinate grid to show the y intercept of the function 8 6 4 2 8 6 4 2 2 P 6 2

Given the graph below determine whether each statement is true or false 19 W Ley Statement 3 is a zero of the function 0 is a zero of the function 1 is a zero of the function 2 is a zero of the function 4 is a zero of the function True False O

Which graph is sketched to the right A g x x 1 x 2 B g x x 1 x 2 C g x x 1 x 2 2 1 0

Given the function y x 1 Place a point on the coordinate grid to show the x intercept of the function Place a point on the coordinate grid to show the y intercept of the function 6 2 8 6 4 2 ty 0 2 2

Which graphs is sketched below 0 N A g x x x 3 B g x x x 3 C g x x x 3 D g x x x 3

The graph of f x x with three reference points is shown Which of the following represents points from f x to a point on g x 2 x 4 3 Select three that apply A 5 3 B 5 1 C 3 5 D 4 3 E 2 5 4 2 4 2 O 2 y 4 2 4 X

How is the graph of g x 6x 2 related to the graph of f x x

How is the graph of g x x 1 related to the graph of x x

1 What is the value of r if 2 r 8 3 a 30 b 22 c 18 d 2 Exit Ticket 11 29 2 What is the value of x given the equation 3x 4 19 a 5 b 7 7 c 8 d 45 3 What is the value of n given that 12 6 3n a 2 b 1 3 c 2 d 18

Topic 7 Error Analysis Explain the errors in 3 of the 4 calculations below Then fix where possible 1 2x 18 12 18 18 2x 6 2 x 3 2 2 10 6 2x 10 10 4 2x 2 2 2 x

4 3 x 15 x 15 3 2 x 18 2 x 18x2 x 36 7 2 4x 14 5 2 4x 18 8 10 4 8x 6 10 x 4 2 9 20 7 3x

45 Write a function rule gives the total cost p P pounds of sugar if each Pound costs 0 43 that of

Evaluate x 3x 2x 7 X 2 O x 5x 2 Ox 5x 8 111 Ox 5x 6 23 X 2 x2 5x 8 3 X 2 23 X 2

What is the quotient 6x4 15x 10x 10x 4 3x 2 O 2x 5x 2 2x 5x 2 O 2x 5x 2 2x 5x 2

Use the English and metric equivalents to the right along with dimensional analysis to convert the given measurement to the unit indicated 167 km to mi BILLED 167 km is approximately mi Round to the nearest hundredth as needed Approximate English and Metri 1 in 2 54 cm 1 ft 30 48 cm 1 yd 0 9 m 1 mi 1 6 km

Construct a truth table for the statement p q Complete the truth table below P 9 P 79 T T F F T T F LL F p q PU p q

7 12 2 2x 10 2 14 6x 8 10 x 8 3 11 12 18 3x 9 3 40 X 10 12 10 2x 30

1 2x 6 12 4 3 x 15 Topic 4 Equations with negative coefficients constant terms 2 20 4 6x 3 4 8 2x 5 2 4x 18 6 10 x 4

1 4x 4 12 4 x 12 20 Topic 2 Positive whole number equations 2 3x 4 11 5 2x 8 10 3 6x 10 22 6 3x 9 3

Determine whether or not the sentence is a statement Meet me at 8 00 Is the given sentence a statement OYes because it could be labeled as true or false It cannot be determined with further information Yes because it is a command No because it is a command O O

What type of function is f x 1 Oexponential decay

10 4 3 13 4 7 16 4 10 11 4 2 14 7 8 17 30 6 12 4 8 15 5 6 18 20 5

For f x x and g x x 8 find the following composite functions and state the domain of each a fog b gof c fof d gog a fog x Simplify your answer Select the correct choice below and fill in any answer boxes within your choice OA The domain off og is x Type an inequality Use integers or fractions for any numbers in the expression Use a comma to sepa B The domain of fog is all real numbers b gof x Simplify your answer Select the correct choice below and fill in any answer boxes within your choice OA The domain of g ofis x Type an inequality Use integers or fractions for any numbers in the expression Use a comma to sepa OB The domain of g of is all real numbers 0 fo f x Simplify your answer Select the correct choice below and fill in any answer boxes within your choice OA The domain off of is x Type an inequality Use integers or fractions for any numbers in the expression Use a comma to sepa OB The domain of f of is all real numbers d gogxx Simplify your answer Select the correct choice below and fill in any answer boxes within your choice OA The domain of g og is x

Let G be a group with G pq where p and q are prime Prove that every proper subgroup of G is cyclic

9 5 6i 4 7i 11 10 Section 3 3 What must be added to both sides of the equation to solve by completing the square Solve for x by using the Completing the Square method x 24x 17 9 3i 12 x 16x 36

7 x 12 5 3 5x 40 65 5 x 12 X 7 12 5 subrtaction mulipication x 12 5 7 subtraction addition divison addition x 19 5 x 40 65 3 5 x 11 614 X 12 5 X 7 X 7

Equation 2x 4 35 x 3 45 8 43 7 x 12 5 Operation Guided 1 Step Equations Practice Inverse Operation Work make sure to rewrite equation

No Calculator Solve for the unknown variable in each of the problems below showing your work 2 8 2x 1 x 8 4 a 5 b 2 c 4 a 4 b 4 c 16

Simplify each expression 35m 65n 10 28n 4n 1 A 10m n 1 C 3 n 3 n 1 3n 5m 50n 80 B D n 1 n 9 3 An n 8 2 2 7r 70 5r 39r 54 35r 42 10r A C r 1 r 8 7 6 r 3 B r 10 9 10r D r 5

8 12 8

3 5x 40 65 5 x 12

Example 2 Work 4x 3 5 4 Expl

Consider the following f x x 4x 4 a Use the Intermediate Value Theorem and the table feature of a graphing utility to find intervals one unit in length in which the polynomial function is guaranteed to have a zero Select all that apply O 2 1 O 1 0 0 1 1 2 O 3 4 X b Adjust the table to approximate the zeros of the function Use the zero or ro list Round your answers to three decimal places feature of the graphing util to verify your results Enter your answers as a comma separated

You construct an open box from a square piece of material 36 inches on a side by cutting equal squares with sides of length x from the corners and turning up the sides see figure 36 2x a Write a function V that represents the volume of the box V x 36 v x 2 b Determine the domain of the function V Enter your answer using interval notation 0 00 c Use a graphing utility to construct a table that shows the box heights x and the corresponding volumes V x V x in x in 1 2 3 K

10 2 4 10

9 12 20

7 86

6 4 8

5 12 10

21 6

3 20 4

E 01 2

7 MS 176

What type of function is Oexponential decay exponential growth 0 1 x 2

What type of function is f x 3x 2 exponential decay exponential growth

Choose the best description of the function shown 4 3 2 f x y 5 4 3 2 1 1 2 3 1 2 3 4 5 O exponential decay exponential growth