Quadratic equations Questions and Answers

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

Graph the equation 3 y x 3 x 7 4 1111 9 8 7 6 5 4 3 2 6 88 Y 7 6 5 4 3 2 H 2 3 4 x TTTTT 1 2 3 4 5 6 7 8 9

25 y x 2y 3x 5 y 2z 4 and 1 b y 32 2 and y 32 5 are paralel because the slope of each one is c y 2z 4 and 2X are perpendicular because the product of the spe d y 27 3 and y 2r 3 y 32 3 Section Exercises 44 Exercse 25 y 2x 3 X are perpendicular because the product of the spea y 38 5 Xa perpendicular because the product of the siges y 2 2 23 2 3 2 G

O 1 000 O 100 Cicer Cremy 10 000 Green Grocery Mart Sales Year 2003 2004 2005 To find out exact sales numbers you need to multiply the numbers in the Sales column by 2006 2007 Sales in thousands of dollars 100 110 140 90 130

A ball is thrown upward and outward from a height of 6 feet The height of the ball f x in feet can be modeled by f x 0 1x 0 8x 6 where x is the ball s horizontal distance in feet from where it was thrown Use this model to solve parts a through c a What is the maximum height of the ball and how far from where it was thrown does this occur The maximum height is feet which occurs feet from the point of release Round to the nearest tenth as needed b How far does the ball travel horizontally before hitting the ground feet Round to the nearest tenth as needed c Graph the function that models the ball s parabolic path Choose the correct graph below OA Height 25 20 15 104 sond 5 O B Height 25 20 15 10 5 0 Q O C Height 25 20 15 10 5 04 BE A Q Q OD Height 25 595 20 15 10 5 04 o 5

Graph the following four quadratic functions x x 3 2 g x x 3 2 h x x 3 2 j x x 3 2 10 O CO 8 L ON 11 3 2 10 9 8 7 6 5 4 3 2 1 MAD 1 2 MAN 1 2 3 4 5

Graph the function 1 h x x 1 x 7 9 8 7 6 5 4 3 2 6 Y 1 8 7 6 5 4 3 2 14 2 3 x 1 2 3 4 5 6 7 8 9

Find the vertex y intercept and x intercept s of the parabola that is defined by the following quadratic function f x x 8x 7 Determine the vertex of the parabola in x y form Determine the y intercept of the parabola in x y form Determine the x intercept s of the parabola in x y form If mulitple x intercepts exist enter the points using a comma separated list If no x intercepts exist enter DNE

Myra sells mugs at the sidewalk fair every week Her revenue from selling a mugs is 8x 0 4x dollars and the cost of producing a mugs is 60 5x dollars a Write an expression for the profit Myra earns from selling mugs P b Find Myr s profit from the sale of 5 20 and 25 mugs P when 5 P when 20 when 25 P

1 5 6 B 2 5 L S 1 3 7 9 8 11 12 13 14 15 16 2 5 d 110 5 Y 217 N 2 5 3 0 2 4

Write the equation of a sine or cosine function to describe the graph 7 m 2 5 NT 0

Using complete sentences and correct mathematical terminology answer the following questions A gardener noticed a rainbow through the arch of the stream of water while he was watering his garden He wondered the height of the rainbow and decided he could use the stream of water to determine it The time t the water is in the air is measured in seconds and the water s height w t is measured in inches above the ground The function that represents t relationship is w t 4 9t2 15t 23 1 Correctly interpret the following calculations within the context of the given scenario above i w 0 4 9 0 15 0 23 23 ii a 4 9 b 15 c 23 h 2a 15 2 4 9 1 53

Drag each graph above to match the function below y sinx 1 0 1 Ay 0 T A y cos 2x T G Q y cos x N101N 2x y 2 sinx Ay V I 2x CO ON Ay 2 Ay y sin 2x y 2 cos x U

4 Freshmen and seniors at Southland get out at 3 50 There are 180 freshmen and 100 seniors One day 60 of the freshmen and 80 of the seniors leave the building right away at dismissal How many freshmen and seniors are staying after for an activity in total

Graph the following function over the interval 2x 2 Give the amplitude y 8cos x Which of the following is the correct graph of the function y 8cos x A 16 46 X B 16 16 K NE What is the amplitude of the function 8cos x function Type an integer or a simplified fraction Q 5 OC 2 16 x 12x Q G OD Save 2x C

6 Pat spent 20 of the money in his bank account on a new phone If the phone cost 300 how much money does Pat have left

Graph the following function over a two period interval Give the period and the amplitude y sin 4x What is the period of the function y sin 4x I 2 of 1 Save Simplify your answer Type an exact answer using x as needed Use integers or fractions for any numbers in the expression What is the amplitude of the function y sin 4x Type an integer or a simplified fraction

2 Lisa has a bag containing 60 potato chips She eats 80 of the chips and saves the rest for later How many potato chips are left

K Determine the amplitude of the function y 4 cos x Also choose its graph The amplitude is 4 Choose the correct graph O A OB GEETSS Q O C OD O OU

Graph the following function over a two period interval Give the period and the amplitude 1 y cos x 1 What is the period of the function y cos 7x 10 MG 2 Simplify your answer Type an exact answer using as needed Use integers or fractions for any numb e expression WIENA GIVEN VERS ENDEAVE WESTEN MASS SEA TO CON TENDRESSE MAN SE ELE Par NESTAR W S S CHEREAFUATO D MATANG PE D C D www comww Se D NO C D PRENSANTO Tse gang med an SEMANG PODER W lata TOLERAN S Bes THE PO Sempres S SE bod Mercede CONSER

10 8 Solve this expression A 28m n B 28m n 1 C D 28m n 28m5 n 4m n 7m n m n7

Simplify the complex rational expression using either Method I or Method II 2 n 2 n 9 n n 3 2 n 2 n 9 n 2 n 9 n n 3 1 n 3

Simplify the following complex rational expression using either Method I or Method II 1 15 X 4 1 15 3

Simplify the complex rational expression using either Method I or Method I N CO 8 1 64 8 N CO 64 N 1 Z 11

Simplify the complex rational expression using either Method I or Method II N 2 4 t t 2 1 2 4 2 t 4 t t 2 1

Simplify the complex rational expression using Method I or Method II X 4 X 4 X 10 X 2 1 2 Y 2 x 4 x 10 1 X 4 X 2 2 x 2

Simplify the complex rational expression using either Method I or Method II 7 X 49 X 7 3 1 1 X

Graph the equation 2 3 2 y x 7 x 1 9 8 7 6 5 4 3 2 84 7 6 5 3 2 3 x 1 2 3 4 5 6 7 8 9

Simplify the complex rational expression using either Method I or Method II 2x 3 x 4 X 4 X 6 2 x x 34 2x 3 X 4 2 x x 34 T x 4 X 6 11

Simplify using Method II x 4 X 4 x 6 x 2 4x 2 II x 4 x 4 x 6 x 2 4x 2 x 2 1

Simplify the complex rational expression using Method II x 3 x 9 X 5 2 1 x 3 x 9 1 X X 5 2 X 9

following question Click here to watch the video Simplify the expression using Method I d 2 2 d DIN d 2 4

Use the given zero to find the remaining zeros of the function h x 3x4 8x 9x 32x 12 zero 2i The remaining zeros of h are

2 3 4 5 6 7 T8 9 10 11 12 13 V IV 200m in VI A B C D WATCH THE LETTER UNCER EACH SYMBOL WITH THE CONNECT WORDING GREATER THAN LESS THAN AT MOST AT LEAST NO MORE THAN NO LESS THAN 14 15 16

2 Students in a ninth grade class measured their heights h in centimeters The height of the shortest student 4 was 155 cm and the height of the tallest student was 190 cm Which inequality represents the range of heights 1kc6 114 439 koks20 A 1500

Perform the indicated operation 2 356 c6 1066

Perform the indicated operation 7w 6 w 5w 6 w w 2

Perform the indicated operation 12a 132 a 5a 14 12 2 a

Perform the indicated 7d d 1 10 d 4 operation 4d 10 d 3d 4

5p 5p 6 21p 18 5p 6 Reduce your answer to lowest terms Add

Add 44a 8a 9 4a 45 9 8a Reduce your answer to lowest term

Draw the complete shearing force diagram for the cantilever beam shown below 4m 4 kN m 2 m

Figure 4 21 suggests one way to prove that 2ab a b a b 2 ab E A C Figure 4 21 Prove these inequalities assuming that AC a and CBR h B

Use the graphs of f and g to describe the transformation from the graph off to the graph g f x 1 x 5 g x f x 3 The graph of g is a translation unit s of the graph of f

Solve the following polynomial equation given 5 is a zero of f x x 9x 23x 15 T 9x 23x 15 0 The solution set is

y 3 8 x 5 x 3 9 8 7 6 5 4 3 2 Y 9 8 7 6 5 4 34 2 1 A 2 3 4 5 6 7 8 9 6 x 1 2 3 4 5 6 7 8 9