Quadratic equations Questions and Answers

What is the y value of the vertex of the following f x 24x O O O O O O 8 6 6 8 2x 7 79 none of these

square you will need to undo a squared term at some point How is this accomplished divide both side by the square root subtract the number under the radical from both sides take the square S root of both sides squaring both sides it cannot be done Your answer is already

What value of c will complete the square x x c O O 2 none of these choices 1 2 1

Solve by factoring x 11x 137 2 O O O O 6 18 7 18 12 18 7 19 11

Factor each Perfect Square Trinomial 11 16x 40x 25 2

1 point A grocery store chain has been tracking data on the number of shoppers that use coupons The data shows that 71 of all shoppers use coupons 36 times out of 40 these results were considered accurate to within 3 5 What is the margin of error 0 025 0 71 0 035 D 0 29

1 point A grocery store chain has been tracking data on the number of shoppers that use coupons The data shows that 71 of all shoppers use coupons 36 times out 40 these results were considered accurate to within 2 5 What is the confidence level 99 95

Properties of Logs Rewriting one log as multiple logs is an example of Rewriting multiple logs into a single log is an examp expanding condensing

The equivalent exp Look at the Example Suppose the club increases the selling price of a frame to 13 Write an expression with exactly two terms for the amount of money the club will make for selling fframes Show your work 13 2 11 V e

Solve the equation Round your answer to 3 decimal places e x 2 5 X

Determine the domain and range of the 5 co 2 5 4 2 b 1 1 0 1 2 3 1 N 2 Domain 4 3 Range 5 5 Domain 4 3 Range 5 5 3

The equation p 100 000 0 8 represents the population p of migrating butterflies w weeks since they began their migration 5 1 Is the population growing or decaying Explain your thinking 5 2 By what percent is the butterfly population changing each week 5 3 What will the population be after 5 weeks A book sold 600 000 copies the year it was released Each year the number of copies sold decreased by 50 7 1 Write an equation that represents the number of copies c sold t years after the book was released 7 2 Use a graphing calculator to determine the value of c when t 6 Explain what it means in this context The equation A 5 000 1 25 represents the area of a forest in acres A where d is the number of decades since 1950 6 1 is the area of the forest growing or decaying Explain your thinking 6 2 By what percent is the area changing each decade 6 3 What was the forest s area after 4 decades Scientists tracked the population of bees p t in a county for t years They wrote the equation 100 000 0 82 to represent their findings p t 8 1 Describe what each number in the equation represents in this situation 8 2 Calculata p 3 Explain what that means in this context

Write and simplify a polynomial with 4 31 and 0 multiplicity 2 as roots Write your answer in standard form

1 point Mr Mitchell was interested in the effects of music on student performance At the bottom of his exam he asked students to circle their favorite type of music rock country or hip hop He then computed the averages for the students who liked each type of music and compared the results Is this an experiment or an observational study Experiment Observational Study

1 point Researchers tested a new cleansing product called Protective Daily Wash on 100 randomly selected participants The researcher put 50 participants in Group A and 50 participants in Group B Group A was given instructions to wash their face daily with the product in a commercial bottle which was only distilled water that was then scented to smell like the actual product Group B participants were given the actual Protective Daily Wash product in a commercial bottle and told to wash their face daily with the product This is an example of which type of study Simulation Experimental Study Census Observational Study

1 point The Advanced Algebra teacher wants to know if the students need a study guide for the test What is the best design for data collectic Observational Study Experiment Census Survey

Select all expressions are equivalent to 38 A B C 83 310 32 LL 3 8 D 34 E 3 3 4

An arch of a walkway can be modeled by y 0 06x where x and y are measured in meters Find the height and width of the arch when the arch meets the ground at the points 10 6 and 10 6 Height m Width m M

5 What are the roots of the polynomial function y x 2 x 7 A 2 7 3 B 2 7 multiplicity 3 c 2 7 3 D2 7 multiplicity 3

4 Factor 27x 64 A 3x 4 9x 12x 16 B 3x 4 9x 12x 16 c 3x 4 9x 12x 16 D 3x 4 9x 12x 16

The longer leg of a right triangle is two inches more than twice the length of the shorter leg The hypotenuse is two inches less than three times the length of the shorter leg Find the length of the hypotenuse Type a response

8 Question 8 9 How does a multiplicity of 2 affect the graph A bounce B wiggle C cross

WHAT FACTORING TECHNIQUE YOU HAVE TO USE TO SOLVE FOR THE FACTORS OF 27X 3437 DIFFERENCE OF TWO CUBES B SUM OF TWO CUBES FACTORING BY GCF D DIFFERENCE OF TWO SQUARES

A water balloon is catapulted into the air so that its height h in metres after t secc h 4 9t 27t 2 4 6 How high is the balloon after 1 second zoom in 7 8 For how long is the balloon more than 30 m high What is the maximum height of the balloon

A 1 2 3 4 5 6 7 6 1 point Simplify 8 9a3 72a 3a 36a 3a 72a 3a 8a 3a Previous

8 1 point Simplify 49x y4 7zy 24 5 x y 07 x y Oxyl

7 1 point Use a calculator to approximate each value t 89 9 434 9 434 9 433 9 Previous

Cassie is financing a 2 400 treadmill She is going to use her credit card for the purchase Her card charges 17 5 interest compounded monthly She is not required to make minimum monthly payments Answer parts a through c below a How much will Cassie pay in interest if she waits a full year before paying the full balance Round to the nearest cent as needed

Write an exponential model given the two points 10 140 and 11 240 BELED The model is y Use integers or decimals for any numbers in the expression Round to three decimal places as needed

Interest is compounded semianually Find the amount in the account after the given time Principal Rate of Interest Time 3000 6 3 years The amount in the account is Round to the nearest cent C

Find the amount in the account for the given principal interest rate time and compounding period P 1 200 r 2 1 t 7 years compounded continuously 1 0 Type an integer or decimal rounded to the nearest cent as needed A

Paisley found the following measures for the dimensions of her store 17 ft 24 ft How many square feet of carpet will Paisley need for her store O 459 square feet O 648 square feet O 41 square feet 27 ft O 408 square feet

The height of a parallelogram must be O parallel to O the same length as Operpendicular to O longer than its base

What is the formula for the area of a parallelogram 04 bh OA bh OV lwh OV lwh

2 The polynomial p is a function of x The graph of p has four zeros at 4 Select all the expressions that could represent p A 3x x 4 x 7 x 9 B x x 4 x 2 x 9 C 3x x 4 3x 2 x 9 D 3x x 4 2x 3 x 9 E 3x x 4 3x 2 x 9 0 and

2 Solve for x expressed as a mixed radical Show your work 3 b x 72 a x 80 x 180 316 55 c x 256 5 marks

4 Simplify Show your work express answers in exact value Remember BEDMAS a 3 2x 5x 8x b 8 16 10 3 18 c 3 6 4 3 e 2 3 7 5 5 3 45 d x 2 3 h 2 16 m

Use the following information to answer questions 1 and 2 George is standing on the top of a 275 foot building He throws a ball straight up into the air The ball s initial velocity is given as 48 ft sec The height in feet of the ball after t seconds is given by h 16t2 48t 275 1 How long will it take for the ball to reach its maximum height above the ground 2 What is the maximum height that the ball reaches Use the following information to answer questions 3 5 Shelly is standing on a platform 100 feet above the ground She tosses a baseball straight up into the air The formula h 16t 64t 100 models the ball s height h above the ground t seconds after it was thrown 3 How long will it take for the ball to reach its maximum height above the ground 4 What is the maximum height that the ball reaches 5 How many seconds does it take for the ball to finally hit the ground rounded to the nearest tenth of a second Use the following information to answer questions 6 8 Les is standing on the ground He launches a model rocket straight up into the air The formula s 16t 64t models the rocket s height s above the ground t seconds after it was launched 6 How long will it take for the rocket to reach its maximum height above the ground 7 What is the maximum height that the rocket reaches 8 How many seconds does it take for the ball to finally hit the ground rounded to the nearest tenth of a second

3 Express as an entire radical Show your work a 3m 7 b 26 c 2x y 3xy 6 man

Which statement describes the graph of f x 4x3 28x2 32x 64 The graph touches the x axis at x 4 and crosses the x axis at x 1 The graph touches the x axis at x 4 and crosses the x axis at x 1 The graph crosses the x axis at x 4 and touches the x axis at x 1

How many solutions exist for the mixed degree system graphed below three zero one two X

Use synthetic division to solve 2x 4x 35x 15 x 3 What is the quotien 2x 2x 29 102 X 3 2x 10x 5 2x 2x 29 1 3

4 The degree of the function is A the size of it B the greatest exponent on the variable C the number of terms

What is the completely factored form of x 64x x 4 x 4 x 4 x x 8 x 8 x x 8 x 8

1 How many roots or zeros does the equation f x 5x 8x 4x 6x 3 have A O B 4 5 D 3

Guided Example 1 Solve the system of equations and list your solution as an ordered pair y 2x 4 y 4x 2

Learning Target I can solve a system of equations by graphing and finding the intersection point of my lines Model Find the solution to the system of equations below 3x y 1 RY 2y 4

Convert to logarithmic form log 7 216

The table shows the height in centimeters that a weight bouncing from a spring would achieve if there were no friction for a given number of seconds Time s 0 0 75 1 5 2 25 3 3 75 4 5 5 25 6 Height cm 0 15 0 15 0 15 15 0 From its resting position how long does it take the weight to bounce one direction then the other and then back to its resting position Enter your answer in the box

The graph shows how many meters above a stream y that a bucket on a water wheel is rotating for a given number of seconds X How many degrees is the bucket rotating in 10 s Enter your answer in the box 18 16 14 12 64429886 10 y 2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36