Quadratic equations Questions and Answers

x 6 4x 8x 3

2x 23x 11 5 9x x

1080 cubic V Lwh 1080 22 2x 19 2x x 49x38x 4x 418 82 4x x 418 1 19 1080 418 Xx 1080 82x 4x3

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 6 4 2 6 1 4 2 0 2

6x5 13x 2x 11x 10x 9x

9x 8x 2x 2x 1 x 4

Add or subtract the following polynomials 4x4 3x 14 3x4 14x 8

8x 3x 1 x4 4x4 x 17

Given the graph of the polynomial function write the function as g x in intercept form y 4 2 O 2 X

A wooden board is leaning against a house The base of the board is 10 feet from the base of the house and the base of the board forms a 35 angle with the ground What is the length of the wooden board Enter your answer rounded to the nearest tenth in the box 17 3 ft

What is the value of cos C of 60 8 B 15

logam x and logany Prove log mn log m log n Drag the statements and reasons into the boxes to correctly complete the proof Statements 2 a m and a n 3 mn a a 4 mn a z y 5 log mn log a z y 7 6 log mn x y log a 8 log mn logm log n log mn log m log n Reasons 1 Given 2 Definition of logarithms 3 Multiplication 4 Exponent rules 5 6 Power property of logarithms 7 Logarithm property log m 1 8 Substitution log m x and log n y log mn x y log mn a x y

What is the logarithmic form of 9 81 O logg 2 81 O logs1 9 2 log 81 2 O log 2 9

Which expression correctly shows how to rewrite log115 using a log base of 8 log118 log 8 O log 5 log 11 log 11 log 5 log 8 log 8

3 7 to search 4 O O 5 6 Which of the following equations has NO SOLUTIONS O 7 8 2 4 3 2 O 2 34 4 2 224 Et 9

Solve for x In 5x 3 2 x Ox O x 1 e 3 5 5 e2 3

22 2a 2 2 4 4 6 4 6 a 2 3a 5 6 r 2 5r 1 3 5 v 4 6 v 7 3

3 5 Solve show work Write your answers as complex numbers your answers should have P in them 3 x 3 25 0 4 x 6x 12 0

Find all values of x that make the equation true Find all values of r that makro the equation truo x 6 3x 9 X X 1 x 3 Sh Show your thinking

n true X x 6 3x 9 x 1 x 3

Which figure below is a graph of r x Letter 10 8 6 10 8 6 4 represents the function r x because 6 Y 2 2 2 2468 6 8 469 2 4 2 4 6 8 6 8 Describe why X 10 8 d 6 10 8 6 4 6 4 22 4 6 8 6 4 2 4 22 6 8 2 4

Simplify 5 27 O 15 3 O 15 3 31 3 O 3 3

Here s the quadratic formula For any equation in the form ax bx c 0 x b b 4 a c 2 a Helpful worked examples Workbook pg 124 and pg 131 1 2 Determine how many REAL solutions the following functions have 1 7x 2x 8 0 2 x 2x 1 0

Which of the following equations has NO SOLUTIONS O O O O 4 x x 1 3 x 1 4 x x 1 4 1 X X 4x x x 1 2 1 2x x x 1 6 x 1 28 830 X 80

Which of the following equations has NO SOLUTIONS O O O O 5x x 2 7 10 x 2 10 2 2 7 2 2 X 3 7 x 2 x 2 5x 5 2 7 252

3 Solve each proportion 8 6 5x 2 5x 9 1 3 5 11 n 7 4 2n 10 5 3 7 2a 6 a 2 11 2 4 6 4 6 a 2 3a 5 4 6 x 2 3 11 5x 1 5 v 4 6 11 V 7 3

7 Which of the following equations has NO SOLUTIONS O O O O 1 4 3 2 4 x 4 2 4 1 2x 4 2 2 4 x 4 4 X 2x 2 4 3x x 4 1 3x 4 2 32 x 4 x 4

The grain stored inside a cylindrical silo is transferred to a transport container in the shape of a triangular prism The container s trangular base has side lengths 5 8m 5 8 m and 8 1m and height 7 2 m The silo has a radius of 5 83 m 30The cylinder has radius 3 cm height 18cmEach ball has radius 3 cma Find the volume of grain that will be removed from the silo if the container is completely filled b Find the amount by which the height of grain inside the silo will decrease Give your answers to an appropriate degree of accuracy

Write a 3rd degree polynomial function with real coefficients having the zeros of 1 and i

orm a polynomial with real coefficients having zeros 2 2 and 3i

Given the graph of the polynomial function write the function as g x in intercept form y 2 X

x 6x 16

5 000 4 000 3 000 2 000 1 000 2 6 8 10 number of years 4 12 14 The graph shows the yearly balance in dollars in an investment account What is the initial balance in the account VE

7 Given the line L x y z 1 0 1 t 1 1 1 the plane P 2x y 2z 7 and the point Q 2 0 1 J X t y ter a Find the distance between the line and the X axis b Find the point A on the plane P which is closest to the point Q c Find parametric equations of the line which intersects both the X axis and the line L at a right angle

Which answer describes the transformation of g x log x 3 1 from the parent function f x log r O It is the graph of f x shifted 1 unit right and 3 units down O It is the graph of f x shifted 3 units right and 1 unit up O It is the graph of f x shifted 3 units right and 1 unit down O It is the graph of f x shifted 3 units left and 1 unit up

Which graph represents f x log x 1 O f x 6 5 4 3 2 2 11 2 3 5 f x 6 5T 4 34 2 14 2 11 2 3 4 5 3 4 5 6 7 8 9 10 st 4 5 6 7 8 9 10 f x 6 5 4 3 2 1 2 11 2 3 4 5 f x 6 5 4 3 2 2 11 2 3 23556 5 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 X x

Given the parent function g a log a What is the equation of the function shown in the graph Of a log 4 2 Of a log x 3 2 Of a log a 2 f x log x 3 4 7 0 A f x 1 X 3 4 6 4 2 7 0 8

What is the equation of the vertical asymptote of h x 6log x 3 5 Enter your answer in the box X

5 7x 4x

5 7x 4x 3

609 9

5 18 13

SE

5 17

5 98

5 3y 24y 21

8 h 25

4 2r 17r 8

2 k2 5k 14

6 3x 21x 30