Questions on Algebra: Quadratic Equation answered by real tutors!

Tutors Answer Your Questions about Quadratic Equations (FREE)

Question 28731: What is the greatest common factor of the terms 14c^2d and 42c^3d?
Click here to see answer by Nate(3500)

Question 30184: i need to complete the square to write the equation so that the right side is in the a(x-H)2 or (square) form and give a graph for the function. p(x)=2x square-2x-24. I tried to do it by dividing by the common factor of 2(x-1)-12,but the answer in the book is, p=2(x-1/2)2 (square)- 49/2 or (.5-24.50 how did they get this. thank you sadie
Click here to see answer by venugopalramana(3286)

Question 30195: when a question asks you to show something algebraically, DO NOT substitute numbers for the variables and give me an example. On the other hand, when a question asks you to show something numerically or to provide an example, you may substitute numbers for the variables. Show all work.
1. Let .
a. Plot z in the complex plane.
b. Compute |z|.
c. What is the angle between the real axis and the line segment joining 0 and z? (Hint: think reference triangle.)
Click here to see answer by venugopalramana(3286)

Question 30207: when a question asks you to show something algebraically, DO NOT substitute numbers for the variables and give me an example. On the other hand, when a question asks you to show something numerically or to provide an example, you may substitute numbers for the variables. Show all work.
Solve for t: 2t(sin(t2+1) + cos(t2+1))2 - 4tsin(t2+1)cos(t2+1) = 2. (Hint: remember that [sin(x)]2 is usually written sin2(x); now look for a trigonometric identity.)
Click here to see answer by sdmmadam@yahoo.com(530)

Question 30638: write the equation of a parabola that opens downward with an axis of symmetry of x=5/2. include a graph of the parabola
Click here to see answer by sdmmadam@yahoo.com(530)

Question 30642: I need to know the vertex and how to graph it. Thank you.
y=-2(x-3)(x+1)
Click here to see answer by Fermat(127)

Question 30649: The length of a rectangular garden is 5 feet greater than the width. The area of the rectangle is 300 square feet. Find the length and the width.
Click here to see answer by Paul(988)

Question 28993: This is a quadratic function problem please show me the steps

John has 128 meters of fencing material with which he wants to make a rectangular pen. If he uses the side of his house as one of the walls, find the nmaximum area he can enclose and the dimensions.
Click here to see answer by checkley71(8403)

Question 30689: This is my original question and I keep coming up with the same answer as the tutor but my book says the answers are -5 and 2. Is that possible?
2x^2-x=1 original equation
2x^2-x-1=0 set the equation to zero
2x^2-2x+x-1=0 the product leading coefficient and the constant is -2 (two numbers that add up to -1 and are multiplied to get the -2 is: -2 and 1)
(2x^2-2x)+(x-1)=0 start to combine
2x(x-1)+1(x-1)=0 take out the factors
(2x+1)(x-1)=0 set them to zero
2x+1 = 0 ; 2x = -1 ; x = -1/2
x-1 = 0 ; x = 1
1 and (-1/2) are your answers
Click here to see answer by Earlsdon(6294)

Question 30763: Publishing costs. The cost, in dollars, of publishing x books is C(x)=40,000+20x+0.0001x^2. How many books can be published for 250,000?
Do I set 40,000+20x+0.0001x^2=250,000 then subtract the 250,000 so the equation =0 and then use the quadratic formula to solve? Could someone show me the correct equation for this problem?
Thank you!
Click here to see answer by mbarugel(146)

Question 30765: Solve the quadratic equation by using the quadratic formula.
This is what I get:
2x^2+4x=-1
2x^+4x+1=0
x=[-(4)+or- sqrt(4)^2-4(2)(1)]/[2(2)]
x=[-4+or-sqrt16-8]/4
x=[-4+or-sqrt8]/4
my answer x=[-4+or-2sqt2]/4
my bookk says its:
x=[-2+or-sqrt2]/2
How do they get there?
Click here to see answer by mbarugel(146)

Question 30795: Question:
The area of a rectangle is 4m^2 and its length is 3m longer that its width. Find the dimensions of the rectangle.
Click here to see answer by troyapplehelen(46)

Question 30792: Please help.
the Question is : find the x and y intercepts for the graph of the equations.
Y=2x^2-9x=4. A graph in included in the question.
the method that is being used by my teacher is where we solve for y( crosses y axis when x=0). In this case y=4. But i get confused factorising to find x.

Click here to see answer by troyapplehelen(46)

Question 30794: This question is really confusing, my tutor ended up answering it in class but everyone was still kinda dazed when we left class. Will you please try to explain or solve this in a manner that is within a students grasp.
Question:
When the first n positive integers are added together, their sum is given by:
1/2n(n+1)
a) Demonstrate that this result holds for the case n=5.
b) Find the value of n for which the sum is 105.
c) What is the smallest value of n for which the sum exceeds 1000?
The chapter we are working on is based on factoring. Please help.
Click here to see answer by Fermat(127)

Question 30641: What the vertex and how to graph it. Please and Thank you.
y=-2(x-3)(x=1)
Click here to see answer by troyapplehelen(46)

Question 30536: when a question asks you to show something algebraically, DO NOT substitute numbers for the variables and give me an example. On the other hand, when a question asks you to show something numerically or to provide an example, you may substitute numbers for the variables. Show all work.
1. Let .
a. Plot z in the complex plane.
b. Compute |z|.
c. What is the angle between the real axis and the line segment joining 0 and z? (Hint: think reference triangle.)
Click here to see answer by venugopalramana(3286)

Question 30981: Fireworks are shot upward with an initial velocity of 30 feet per second from a platform 3 feet above the ground. How long will it take the rocket to hit the ground?
Click here to see answer by Paul(988)

Question 30982: A person springs off a 12 foot high diving board with a 0.0 initial velocity. How many seconds does it take for the person to hit the water?
Click here to see answer by Nate(3500)

Question 30990: how do you solve this equation? (x-7x)squared=5=0 its a quadratic equation(completing a square)
Click here to see answer by ikdeep(226)

Question 30991: will you please solve this equation? xSquared-7x+5=0(Completing a square)
Click here to see answer by Fermat(127)

Question 30987: Solve equation

Click here to see answer by ichudov(499)

Question 31093: What is the minimum product of two numbers whose difference is 4? What are the numbers?
This is a far as I got...
x(x+4)
x^2+4x+c=0
-4/2=-2
2^2+4(-2)+c=0
4-8+c=0
-4+c=0
c=4
x^2+4x+4=0
(x+2)(x+2)
x=-2 and -2+4=2
This is where I realize that something is not quite right...
Click here to see answer by venugopalramana(3286)

Question 31181: Could you solve something like:
3x^2+8x+92

Click here to see answer by longjonsilver(2297)

Question 31185: the larger of two positive numbers is 5 more than the smaller. the product of the number is 36. find the number
Click here to see answer by Paul(988)

Question 31184: the larger of two positive numbers is 5 more than the smaller. the product of the number is 36. find the number
Click here to see answer by joey_quizan(15)

Question 31251: Hi! I need to find all real solutions of this equation:
x^6-2x^3-3=0
I don't think there are any real solutions as I can't factor it right (x^3+1)(x^3-3)=0.
Thank you all so much!
Click here to see answer by longjonsilver(2297)

Question 31275: I have a work sheet with quadratic equations and i don't understand it at all. It read's: Solve the equation by factoring, 3xsquared+9x-12=0.(how do i factor this where do i start?)my teacher showed me how but i can't remember can you please help me?
Click here to see answer by mukhopadhyay(490)

Question 31338: find two consecutive positive intergers such that the square of the smaller increased by four times the larger is 64.
Click here to see answer by Paul(988)

Question 31340: the square of a certain number minus nine times the number is 36. find the number.
Click here to see answer by Nate(3500)

Question 31339: find two consecutive integers such that the sum of their squares is 61.
Click here to see answer by Nate(3500)

Question 31337: in a rectangular garden whose area is 24 Square centimeters, the length is 5 centimeters more than the width. find the dimensions of the garden.
Click here to see answer by Nate(3500)

Question 31335: in a rectangular garden whose area is 24 centimeters, the length is 5 centimeters more than the width. find the dimensions of the garden.
Click here to see answer by Nate(3500)

Question 31334: the square of a certain number minus nine times the number is 36. find the number.
Click here to see answer by stanbon(57984)

Question 31333: find two consecutive integers such that the sum of their squares is 61.
Click here to see answer by checkley71(8403)

Question 31323: Hi,
I'm trying to find all real solutions to this equation:
4x^-4-16x^-2+4=0
I have:
4/x^4-16/x^2+4=0
multiplying by x^4:
4-16x^2+4=0
4x^4-16x^2+4=0
4(x^4-4x^2+1) = 0 (unfactorable?)
a=1;b=4;c=1
Using the quadratic equation I get:
-4+-sq root of 3, but this doesn't seem right.
Thanks for all your help!
Click here to see answer by longjonsilver(2297)

Question 31365: The axis of symmetry of a parabola is the line x=2. The point (4,-4) lies on the parabola. Use the symmetry of a parabola to find a second point on the graph.
Could someone tell me if I am supposed to be using a formula to solve this? I can't figure it out and feel like I'm overlooking the obvious!
Click here to see answer by stanbon(57984)

Question 28934: Hi,
I'm currently studying solving quadratic inequalities, and I'm having a bit of trouble.
I'm trying to solve 1/2x^2 + 3x (less than or equal to) -6. Since I couldn't factor the equation, I tried using the quadratic formula, however I got a complex number. I'm not exactly sure how to test the complex numbers, so I'm a bit lost on how to solving this.
Thanks for any help you can provide!
Click here to see answer by Fermat(127)

Question 31462: HI... I cannot figure this out...
Solve the equation by using athe quadratic formula. Give only real number solutions....
4n ^ 2 = -6n - 1
Click here to see answer by blubunny01(20)

Question 31457: A manufacturer of microwave ovens believes that the revenue R, in dollars, the company receives is related to the price P, in dollars, of an oven given by the function R(P)=125P-0.25P^2. What price of an oven will give the maximun revenue?
-(b/(2a)=
-(125)/(2*-.25)=
-(125/.5)=250
Price of an oven=$250.00
This answer matches my book but my question is doesn't 250= the x coordinate of the vertex and then shouldn't I be solving for the y coordinate to get the maximum revenue? Meaning why don't I then substitute 250 for x and solve for y or am I confusing the use of the phrase "maximum revenue" with a maximum value of a quadratic function problem?

Click here to see answer by stanbon(57984)

Question 31450: using the quadratic equation x2-4x-5=0 perform the following task:
solve by completing the square.
how do i do this im lost thank you.
Click here to see answer by Earlsdon(6294)

Question 31425: 1. 2x^2 - 7x + 5 =0
2. 3x^2 + 10x + 5 =0
3. -5 + or - the square root of 10 / 3

Click here to see answer by ikdeep(226)

Question 31494: Let p,q be the roots of the equation (x-a)(x-b)=c with c<>0.Then the roots of the equation (x-p)(x-q)+c=0 are which of the following:-
A.a,b
B.a,c
C.b,c
D.a,b,c
Click here to see answer by mukhopadhyay(490)

Question 31632: 3) Suppose you throw a baseball straight up at a velocity of 64 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0
• 16 represents 1/2g, the gravitational pull due to gravity (measured in feet per second2).
• v0 is the initial velocity (how hard do you throw the object, measured in feet per second).
• s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.
1. How long will it take to hit the ground?
2. What is the maximum height of the ball? What time will the maximum height be attained?

Click here to see answer by Earlsdon(6294)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250, 20251..20295, 20296..20340