Quadratic equations Questions and Answers

Answer Check Identify the axis of symmetry Write as the equation of a line y 2 x 1 1 Answer Check Identify the maximum or minimum y 2 x 1 1 Select one O a maximum 1 O b maximum 1

Use synthetic division to show that x is a solution of the equation and use the result to factor the polynomia x 28x48 0 x 4 I

3 Find the factored form Use imaginary numbers to write as the product of two binomials 4b 1

For the parent function of f x x write an equation using the following transformations then graph it 3 Vertical reflection Vertical stretch by 3 Horizontal shift by 4 Vertical shift by 5 4 2 4 a Vertical stretch by 2 b Horizontal reflection c Horizontal stretch by 3 c Horizontal shift by 6 11 10 4 10 9 8 7 6 54 2

Solve using the quadratic formula Only need to input the final answer Leave in radical form when applicable a 3x 36 0 b x 14x 53

Select one O a 5 71 24 O b 1 4 2 3 c 2 3 O d 1 4 2 3 Check the exact X A AVAN 5X Solve using the quadratic formula Input answers from least to greatest x 25 0

Consider the polynomial below Find f 2 by using synthetic division and the Remainder Theorem and by evaluating f 2 directly Use Remainder Theorem f 2 f x 2x 2x x 4 Evaluate Directly f 2

4 Use a calculator to graph and solve If exact roots cannot be found approximate to the nearest hundredth x 2x 2 0 5 Use the formula h t 1622 vt ho Melia throws a softball with an initial velocity of 32 feet per second She releases the ball at about 4 feet above the ground How long it take for the ball to reach the ground Round to the nearest tenth Show steps or explain how you found the answer 6 Write a quadratic equation and solve to find two real numbers such that their sum is 8 and their product is 209 Show or describe steps

Find the discriminant for x 2x 5 0 Select one a 24 O b 16 c 24 O d 16 Check Find the value of the discriminant for each quadratic equation Then describe the number and type of roots for the eq x 8x 16 0 Choose 3x 2x 0 5x2 6 0 x x 1 0 Choose Choose Choose

Which is the graph of the equation y 0 0 0 0 a Ob C Od T a IL 4 2 3 1 4 6 2x 2x 2 d 4 DETT

3 y x 2x 5 a Write the function in vertex form b Find the axis of symmetry and vertex c Is the vertex a maximum or minimum How do you know

The quadratic formula can be used to solve any quadratic equation Select one True O False Check Match the value of the discriminant with the number of roots for a quadratic equation ax bx c b 4ac 0 6 4ac 0 Choose Choose C

1 Show steps to solve each equation by the Square Root Property Other methods will not earn credit a 36x 12x 1 b 2x 20x 50 128 18

The path that an object travels when influenced by gravity is called a trajectory and trajectories can be modeled by quadratic funct h t gt vt ho What does each variable represent in the given formula h t Choose g V t ho Choose Choose Choose Choose Check The acceleration due to gravity is meters per second

Consider the polynomial below a Find all the rational roots Separate your numbers by commas Repeat roots in the list when necessary list of rational roots P x x 4x 3x 14x 8 b Express P x in factored form with the leading coefficient factored to the front P x

4x 28x 49 5 Input answers as decimals rounded to the nearest hundredth least to greatest X

Rewrite the equation in vertex form by completing the square Then determine the vertex Input vertex x y or y x 4x 1

Find the value of c that makes each trinomial a perfect square Input fractions in simplest form a b a x 10x c C b x 9x c C Check Determine whether the value of c that makes ax2 bx c a perfect square trinomial is sometimes always or never negativ O always O sometimes Onever O not enough information Check What is the vertex of the quadratic function below y 3 x 2 2 1 O 2 1 O 2 1

Solve by completing the square 3x 7x 5 9 b Oa Ob Od 7 6 3 109 6 109 3 d 7 t 3 m 10 3

Consider the polynomial below a List all potential rational roots using the Rational Root Theorem Separate your numbers by commas list of possible rational roots P x 7x 29x 31x 5 b Find all the rational roots Separate your numbers by commas list of actual rational roots c Express P x in factored form with the leading coefficient factored to the front P x

Check 9x 12x 4 4 X M Check

Q3 Sketch each of the following sets of points in the complex plane separately i e four different sketches for a d After sketching each set determine if each of the sets are i open ii connected iii bounded iv domain 15pts 4 If All correct a Re 3 i z 1 2 b 2 2 14 4 c Im 2 Re z 1 4 d 2 z 4 3i 2 4

8 A coastal geologist estimates that a certain country s beaches are eroding at a rate of 1 5 feet per year According to the geologist s estimate how long will it take in years for the country s beaches to produ

7 Wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour Based on this information what is a possible amount of time in hours that it could take Wyatt to husk 72 dozen ears of corn

Suppose that you decide to buy a car for 59 000 including taxes and license fees You saved 11 000 for a payment The dealer is offering you a choice between two incentives Incentive A is 7000 off the price of the car followed by a three year loan at 6 31 Incentive B does not have a cash rebate but provides free financing no interest over three years What is the difference in monthly payments between the two offers Which incentive is the better deal Use PH 9 PMT The difference in monthly payments between the two offers is S Round to the nearest rent as needed

1 3 5 7 9 a c d solve for b 0 0 atb dic an x an xx nn in terms of the given variable b dtc a y Box a b x y a fux n d rt d rt 7 1 solve for a solve for r d flexty solve for a atby dxty a Fdxty b b 2 p w b n J P w b C C n p w b solve for n 2 4 6 8 10 xyz n solve for y XZXZ A y mx b y b mx ax b c y kx X by L ax b b y x ab y Y Kx X x Gab q a solve for m y b X 54 solve for k solve for y Im y c ax 5x CK solve for b

Use the table to determine the location of the zeros 2 12375 SARSSONHN 4 Y 7 9 8 5 7 16 27 The smallest root is at x The other root is at x

b vertex write as an ordered pair x y 1 3 x c axis of symmetry x d maximum or minimum Maximum e range o 3 Check at y 3 Partially correct Marks for this submission 2 00 3 00 Accounting for previous tries this gives 1 Given f x 2x2 Identify the following a y intercept write as an ordered pair x y 0 0 x b vertex write as an ordered pair x y 0 0 c axis of symmetry x 0 x

Use the table to determine the location of the zeros of the quadratic function 7 8 6 1 5 4 The smallest root is between The other root is between 4 4 3 1 and and 2 8 22 0 48

2 x x 6 0 a What is the axis of symmetry What is the vertex b What is the solution based on the graph If the exact roots cannot be found state the consecutive integers between which the roo are located Explain your answer c Upload a picture of your hand drawn graph Label vertex and one point on either side of the vertex

1 What are the solutions for the equation Give a reason for your answer x 2x 3 0 y 0 X

1 Use a calculator to graph and then identify the following for the parabola y x 2x 1 a vertex b axis of symmetery c maximum or minimum value d domain e range

2 Show the steps you would use to graph the function without using a calculator y a Find the vertex b Find the y intercept c Find the point on the other side of the axis of symmetry from the y intercept HN 1 2x x 2x 8

Simplify cot t cs t sin t to a single trig function

19 If a 3 pound pizza is sliced in half and each half is sliced into thirds what is the weight in ounces of each of the slices 1 pound 16 ounces a 4 b 6 c 8 d 16

Solving Quadratic Equations By Completing the Squarebate Solve each equation by completing the square 98 28 1 p 14 p 38 0 P 1yp 51 51 3 a 14a 51 0 a2 149 8 8 5 x 6x 8 0 x 6x 7 x 14x 15 x 14x 9 4r 91 7 11 k 4k 1 5 59 59 2 v 6v 59 0 va bv 4 x 12x 11 0 x2 1DX 6 n 2n 3 0 n 20 21 22 8 k 12k 23 0 k 12k 10 x 10x 26 8 12 b 2b 20

O Nate walks 25 meters in 13 7 seconds If he walks at this same rate which of the following is closest to the istance he will walk in 4 minutes e 150 meters f 450 meters g 700 meters h 1 4000 meters

For 1 1 by sketching a triangle find cos sin degrees

What is the factored form of the expression over the complex numbers 42 25g O 2z Siy 2z Sig O 2z 5ty 2z 50g O 2z 5ig 2z Sig O 2z 5g 2z 5g

What are the roots of the equation x 6x11 7x 8 0 Enter your answers in the boxes X or x or

Factor 54x 2 27y 12 Enter your answer in the box

What is the solution of the equation when solved over the complex numbers 2 20 0 Enter your answers as exact values in the boxes

What are the roots of the equation 4x 20x2 24x 0 O O 3 0 2 2 0 3 O O 0 2 3 3 2 0

Factor 9x 27x 45 Enter your answer in the box

P 2 z 1

10 4 1 5 5 0 5 f x 10 Determine the equations of f x and g x that are represented by the dotted transformations of the function h x x f x g x Check

Divide using synthetic division 3 z 6z 14 Z 3 3 z 6z 14

What is the vertex of f x x 4x 3 Standard Form What is the vertex of g x 5x 3

Divide using synthetic division 2 3x 5x 8x 2 1 x 3 2 3 3x 5x 8x 2 3

5 10 5 0 5 5 10 Sketch the graph of g x x 3x 4 Explain how you graphed it below VE Share With Class