Quadratic equations Questions and Answers

Given that 2 2i is a zero factor the following polynomial function completely Use the Conjugate Roots Theorem if applicable f x x4 3x 8x 8x 96 nswer 2 Points f x Keyba

Write a formula for the function g x described as follows 1 X Use the function f x Answer 2 Points Move the function to the left by 3 units and up by 4 units

Given the following matrices if possible determine BA Identify the dimensions of the resulting matrix and fill out the matrix if it exists If not state Not Possible Answer 2 Points A 4 3 120 33 Selecting the check box will replace the entered answer value s with the check box value Entering the dimensions of a matrix will display any boxes necessary to create the matrix X 3 25 B 1 6 1 9 3 Not Possible 35 21 14 Keypad Keyboard Shortcuts

4 8 2 7 4x 2y 9 2z 8x 7y 9 12 z 8x 6y 2 0 X ALLE y 9 9

5 Step 2 of 2 Find an equation for the axis of symmetry of the parabola defined by the given function Write the exact answer Do not round Answer 2 Points Keyp Keyboard Short

rev 6 3 log x 4 if x 4 if x 24 Step 2 of 3 Evaluate this function at x 4 Write the exact answer Do not round If the answer is undefined write Und as your answer f x Answer 2 Points f 4 Keypa Keyboard Shortc

the triangle ABC Verify that the triangle ABC is a right triangle Find its area A 2 7 B 3 5 C 1 0 OA S OC J Sum of the squares of the lengths of the legs of the triangle Square of length of the hypotenuse of the triangle Q To show that the triangle is a right triangle show that the sum of the squares of the lengths of two of the sides the legs equals the square of the length of the third side the hypotenuse Q

Write a general formula to describe the variation M varies directly with the square of d and inversely with the square root of x M 24 when d 3 and x 16 M Use integers or fractions for any numbers in the expression

The elongation E of a spring balance varies directly with the applied weight W see the figure If E 2 when W 18 find E when W 13 BEE P

ite a general formula to describe the variation e square of T varies directly with the cube of a and inversely with the square of d T 5 when a 4 and d 4 fam BE Use integers or fractions for any numbers in the expression

Vrite a general formula to describe the variation A varies directly with x A 8 when x 2 X 11 Type an exact answer in terms of I

Write a general formula to describe the variation z varies directly with the sum of the squares of x and y z 2 when x 6 and y 2 1000

A polynomial function g x with integer coefficients has a leading coefficient of 5 and a constant term of 1 According to the Rational Root Theorem which of the following are possible roots of g x 1 13

Which expression has a value equal to 28 4

If cosB 2 3 then what is the positive value of cos 1 2 B in simplest radical form with a rational denominator

The function of f x 3x 2 has a domain of 3 5 What is the range of f 1 x

Trapezium ABCD has AB 7cm DC 10cm AD hcm Area 51cm 2 Work out the value of h

log2 n 1 log3 n 1 log6 n 1 oldu una g re n logn ka t r 1 2 log25 A D B 2 1 log52 2 1 log25 E C 2 1 log25 1 2 loga

exponential QUESTION Is there an asymptote If so where is it Ex 4 By looking at the graph above list the domain and range of the function 5 y alu s decrease as the x values increase in the example above this is what we call The graph goes down the hill from left to right DOMAIN 8 y 5 RANGE Tell whether the functions below show exponential GROWTH or DECAY 4 6 y 2 9 y 0 7 y 1 10 y 2 3

2 3 1 0 Ex 3 Now let s look at how to graph the exponential function y 1 x 3 2 y x y ESTION Is there an asymptote If so where is it 13 DOMAIN 10 5 4 3 2 10 2 4 efinition 3 Since the y values decrease as the x values increase in the example above this is what w ponential The graph goes down the hill from left to right By looking at the graph above list the domain and range of the function y 2

2 Solve the following system of linear equations using Gauss Jordan Method X 2x2 x3 2 2x1 4x3 x4 5 2x2 x3 2x4 31

3 0 1 2 Ex 1 The function y 3 is called an 2 Now let s look at how to graph the exponential function y 3 y 3 1 3 y 3 3 1 27 exponential y function because the exponent is a t 3

13 Min has 590 000 in an annuity that pays 4 4 per year compounded monthly He wishes to make monthly withdrawals for the next 20 years beginning at the end of this month a Determine the maximum monthly payment that Min can receive b How much interest will he earn over the life of the annuity c Determine the maximum monthly payment that Min would receive if the interest rate were 5 per year compounded monthly d Determine the maximum monthly payment Min would receive if the interest rate were 6 per year compounded monthly

10 Clark built an addition to his house and needs to furnish a new guest room A furniture store is offering a new bedroom set at 99 per month for 12 months If furniture store calculates interest at 17 2 per year compounded monthly how much would the furniture cost on the day of purchase

Let f x 5 sinx Complete parts a through e below a What is the y intercept of the graph of f 0 Simplify your answer Type an integer or a decimal b For what numbers x x x is the graph of f increasing x Type exact answers in terms of Use integers or fractions for any numbe c What is the absolute maximum value of f 5 d For what numbers x 0 x 2x does f x 0 Use a comma to separate answers as needed Type exact answers in terms e What are the x intercepts of f Choose the correct answer below x x X B xx 2kx k is an integer OA k 1 x 2 integer k is an integer

Problem 4 Show that the equation 3x 5y z does not have a solution with 1 x y z integers

A rock is thrown upward from a bridge that is 66 feet above a road The rock reaches its maximum height above the road 0 98 seconds after it is thrown and contacts the road 3 05 seconds after it was thrown Write a function f that determines the rock s height above the road in feet in terms of the number of seconds t since the rock was thrown f t Hint the function f can be written in the form f t c t t t t for fixed numbers c t and t2 Preview

In the Linear Function f x 3x 2 what is the y intercept b 3 b 2 b 2 b 3

In the Linear Function f x 3x 2 what is the slope O Om 3 Om 2 Om 3 2 m

Suppose S is a collection of 59 pairwise distinct vectors in IR59 so any two vectors from S are distinct Then dim span S

A pebble in the tread of an 18 inch tire is rotating at a speed of 25 revolutions per minute What is the speed the pebble is traveling at in miles per hour What is the speed the pebble is traveling in degrees per minute

trees must not exceed 504 The revenue from a single apple tree is 81 and the revenue from a single peach tree is 168 Determine the number of each type of tree that will maximize revenue What is the maximum revenue Let x represent the number of apple trees and y represent the number of peach trees Answer Enter the value in the first box and the ordered pair in the second box Maximum revenue of Maximum revenue at Keyp Keyboard Short

What are the area and perimeter of rectangle CDEF 1 0 8 6 4 Area Perimeter 1044 D 8 C 6 4 2 20 NO 2 4 6 8 10 2 square units units E 4 6 F

What is the area of rectangle CDEF E Area 104 8 6 4 2 6 4 2 0 F 2 4 6 8 1 0 y 2 4 6 square units D X 8C 10

What is the perimeter of AHIJ J 0 8 6 4 Perimeter 1 04 8 6 4 2 20 2 4 6 8 1 0 y units 2 4 6 H

Problem 11 Circle O is inscribed in equilateral triangle ABC Circle P of radius 1 is tangent to circle O and segments AB and BC Find the area of triangle ABC B A 27 B 9 3 C 36 3 D 27 3 E 47

pattern to determine which function best represents the data Then write an equation to model the data X X Y Y 3 32 12 2 16 1 8 Type of Function exponetinl Equation 2 42 0 3 2 1 27 12 3 4 z 2 Look for a pattern to determine which function best represents the data Then write an equation to model the data 0 Y 0 1 2 1 1 2 3 2 1 4 Graph 5 Graph f 6 Graph f Show your

7 9 29 19 ng side 16 33 X 55 8 10 12 X 23 10 68 21 22

Determine if the two triangles are congruent If they are complete the triangle congruence statement and identify the triangle congruence theorem used Convent Yes No ANAABCA Triangle Conarvence Theorem Congoment Yes No KAAYXA Inanale Congmense Theorem Congruent Yes No AHGF A Triangle Congruence Theorem d Congruent Yes No AAGCA Triangle Congrvence Theorem

Find the required information and graph the ellipse Ellipse 126y 9y 8x 131 4x Center 1 7 Vertices 13 7 X 11 7 Co Vertices ODDERNA 0 Foci 1 4 5 7 x 1 4 5 7 x Graph X Clear All Draw W fe 20 W W X 21

Identify the transformation taking place and use slope to justify your answer C D 5 D B C A 5 0 A B

10 2 5x 1 2x 3x 8 a 5 b 9 5 c 2

Determine the amplitude of the following graph 5 4 3 O 31 2 1 3x 720 4x 911 5TK nix 3 5 2 11x 67 2

Solve each equation 1 5 10 500 000

In APQR the measure of R 90 QP 73 RQ 55 and PR 48 What ratio represents the secant of ZQ 55 73 48 Che

In 2005 Capital City determined its population in millions could be expressed by this function P x 05x 53 7 where x is the number of years after 2005 Which of the following statements is true The city s population was 53 45 million in 2005 The city s population was 54 million in 2011 The city s population is increasing at a rate of 05 million each year The city s population is decreasing at a rate of 05 million each year

determine the oblique asymptote of f x 3 2 9x 9x 5x 6x 9 x 6x 5x 9

What type of function is graphed What do you notice about the graphs Can you write the equation of the second graph y

et P be the point given in polar coordinates by 4 5 a Plot P on the polar axes below 61 6 7 6 21 3 4T 3 T 2 31 2 11 3 or the point P 51 3 77 6 1110 Express the point P in polar coordinates with a positive r value and a positive 9 valu

For which values of x is the following matrix invertible x 2 2 4 2 4 1 4 2 x