Quadratic equations Questions and Answers

The profit function for a firm making widgets is P x 132x x 1800 Find the number of units at which maximum profit is achieved X units Find the maximum profit

2 linear power O quadratic cubic 10 8 6 2t 2 6 8 10 X

hine whether the scatter plot should be modeled by a linear power quadratic cubic or quartic function y 000 4 linear power O quadratic cubic Oquartic 2 5 5 10 15 2 4 6 8 X

2 The table shows the total number of segments whose endpoints are chosen from x points no three of which are collinear Number of points x Number of segments y 2 3 1 3 200 a The third point on the table is 4 6 Write a quadratic model of the data What point would go in the last set of missing boxes in the table Show your work b Predict the number of segments that can be drawn using 10 points Show your work 3 Determine whether a quadratic model exist for the set of values If so write the model Show your work f 2 16 f 0 0 f 1 4

1 Find a matrix that generates the weighted inner product u v 3u v 2u2 V2 U3 V3 on R

5 Are the vectors v 1 0 1 v 0 2 0 and v 1 0 1 an orthogonal set with respect to the Euclidean inner product on R If yes find the corresponding orthonormal set

Find a curve of form y a b x that best fits the data points 1 5 2 3 and 3 2 5

6 Find the least squares quadratic fit y ao a x a x to the data points 1 6 0 1 1 4 and 2 7 Compare y values obtained with given y values

118 f x 44x 1 52x 3 floo 14x 152x 3

Complete the following table which shows the performance of two investments over a 5 year period Anjana deposits 3000 in an account that earns simple interest at an annual rate of 2 9 Darin deposits 3000 in an account that earns compound interest at an annual rate of 2 9 and is compounded annually Complete the following table Round to the nearest dollar as needed Anjana s Year Annual Interest Anjana s Balance Darin s Annual Interest Darin s Balance ELLCO Year 1 2345 5 Anjana s Annual Interest Anjana s Balance Darin s Annual Interest Dan Bala

Which is an apparent factor of the quadratic function graphed below 17 B 6 4 2 2 A x 6 OB x 5 OC x 5 OD x 2 Lov X

What are the zeros of this quadratic function f x x 7 x 8 OA x 0 and x 8 OB x 7 and x 8 OC x 0 and x 7 OD x 7 and x 8

From a group of 7 people you randomly select 2 of them What is the probability that they are the 2 oldest people in the group Give your answer as a fraction

8 Simplify the given expression 8x y 8x y O 64x6y4 O 16x64 O 8x4y 8x y

Use the functions f x x 1 and g x x 1 to answer parts a g a Solve f x 0 g Solve f x 1 b Solve g x 0 c Solve f x g x d Solve f x 0 e Solve g x 0 f Solve f x g x

Use the functions f x x 1 a Solve f x 0 b Solve g x 0 c Solve f x g x and g x 5x 5 to answer parts a g d Solve f x 0 e Solve g x 0 f Solve f x g x g Solve f x 1

4 Greg s backyard measures 30 m by 30 m He wants to build a small tennis court that measures 20 m by 15 m 15 m 30 m 20 m 30 m a What fraction of Greg s backyard will be used for the tennis court 3 marks b What percent of Greg s backyard will be used for the tennis court 3 marks

3 In simplest form find the area of the shaded portion of the figure below if x 2 y 4 4 w 2 3 and z 2 All figures are in inches round to the nearest tenth y X

15m 30 m 20 m 8 10 b 30 m a What fraction of Greg s backyard will be used for the tennis court 3 marks b What percent of Greg s backyard will be used for the tennis court 3 marks

11 Simplify the given expression 665 567 36 36

A rain gutter is to be made of aluminum sheets that are 16 inches wide by turning up the edges 90 See the illustration a What depth will provide maximum cross sectional area and hence allow the most water to flow b What depths will allow at least 30 square inches of water to flow X X 16 2x 16

6 Answer the following questions in the space provided 1 Sketch the graph of the function f x Include all asymptote lines on your graph x 3 a Write the equation of the vertical asymptote line

2x 8 x x 6 As x f x 1As x x 1 As x f x 0As x f x 0 Determine the end behavior for f x As x f x 2As x f x 2 As x f x 1As x f x 1

Find all local maximum and minimum values for gx x Local Minimum 0 1 25 Maximum y 1 Local Maximum 0 1 25 No Minimum Local Minimum 0 1 25 No Maximum Local Minimum 2 28 1 25 No Maximum x 5 x 4

The flag of a country contains an isosceles triangle Recall that an isosceles triangle contains two angles with the same measure If the measure of the third angle of the triangle is 45 more than three times the measure of either of the other two angles find the measure of each angle of the triangle Recall that the sum of the measures of the angles of a triangle is 180 H4

A lady wants to make an open top box for packing baked goods by cutting equal squares from each corner of an 10 in by 16 in piece of cardboard as shown in the diagram She figures that for versatility the area of the bottom must be 86 in What size of square should she cut from each corner 2

Find the difference quotient of f x x 4 that is find The difference quotient is f x h f x h h 0 Be sure to simplify

What is the probability that either event will occur First find the probability of event A 6 A B DO 18 12 P A

rag each label to the correct location on the image actor each polynomial function Then use the factors to match each function with the description of its x intercepts One unique point f 2 22 28 98z f 2 32 162 48 Two unique points f 2 2 62 36z 216 f x 2 22 3z 6 Three unique points

Find the domain and range of the function g x sqrt x 2 7x

The graph of f x 3 is reflected about the y axis and stretched vertically by a factor of 4 The coefficient on our transformed function is The exponent on our transformed function is The y intercept on our transformed function is The domain on our transformed function is The range on our transformed function is

I The graph of f x is reflected about the y axis and compressed vertically by a factor of 1

1 Simplify the following polynomia 4xy 2x 2xy 6y 6x 10 O6xy 2x 10 O4xy 10 O6xy 8x 6y 10 O6xy 2x Oy 10

15 Simplify the following polynomial 9x 5x 2x 6 5x 6x

11 Simplify the following polynomial 6c d 4cd 7cd 5cd 8 x

6 Simplify the following polynomial 8 8x 1

13 Simplify the following polynomial 7g h 3gh gh 3gh 1

14 State the degree of the following polynomial 3 2x 2x O 3rd degree O 2nd degree O 1st degree O 4th degree

8 Simplify the following expression 9x 5x 5 4x 3 2 O 11x 5x 15 O 11x 5x 15 O 11x 5x 15 2 O 11x 5x 15

10 Simplify the following expression 7x 7x 6 x 4x 7 Simplified expression

7 Simplify 4x 7x 2x 7 3x 1 ATT

3 Simplify the following polynomial 7a 46 6 2a 4b 8 O 9a 14 O 9a O 9a 2 86 14 9a 86 2

Find the equation of the line that passes through the points 1 0 2 and 0 4 3 a 3 2t t 1 t b 1 2t 3t 2 t c 1 t 4t 2 t d 1 t 2 t t e 2 t 3 t t f 3 t 5 t t

From the given proportional relationship which of the following point lie on the same line 10 8 6 4 2 Y 2 6 8 10

b Find C angle C 5 Use the Cosine law to find the missing side in part a and angle in part b 5 marks a Find c AB 20 b Find A angle A c 27 27 6 Alayna is trying to determine the angle at which to aim her sprinkler nozzle to water the top of a 5 ft tree in her yard Assuming the water takes a straight diagonal path and the sprinkler is on the ground 4 ft from the base of the tree at what angle of inclination should she set the sprinkler Include a diagram of the triangle 6 marks

Let P3 have the inner product given by evaluation at 5 1 1 and 5 Let Po t 1 p t 3t and q t 13 Notice that these polynomials form an 12 orthogonal set with this inner product Find the best approximation to p t 3t by polynomials in Span Po P 9

20 If log x 2 then determine log 125x

Solve the followin problem A hole is cut through the center of a thick sheet of metal The metal is 8 5mm thick 10cm long and 13cm wide The hole was 4cm wide Find the weight of the metal in grams

Which of the following represents the graph of y 10 8 6 4 2 14 420 10 88 6 42 24689 4 6 10 6 8 10 2 x 3

Let f x 5x 2x 4 and g x 4x 5 After simplifying g x