Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 112182: I am given three points on a graph (14,0), (10.5,1), (6.5,3) and am asked to find the equation for the parabola that passes through these points. I understand that the parabola must be positive and open upwards. Also, I know that the "c" value must be 14 because that is the y intercept. But, from then on, I really have no idea what to do. Could you please help me?
Click here to see answer by Edwin McCravy(20054) About Me 

Question 112302: I am not sure which Algebra section this question fits under. Hopefully someone can help me figure this out. I am lost.
I am trying to find the vertex of the function:
f(x)=x^2 -8x -6
Thank you!

Click here to see answer by jim_thompson5910(35256) About Me 

Question 112305: y^2-12y+36=49
c^2+16c+64=15

Click here to see answer by jim_thompson5910(35256) About Me 

Question 112558: x^2+45=-18x
Click here to see answer by josmiceli(19441) About Me 

Question 112615: I am having a hard time writing the formula needed in order to solve this equation; A farmer wishes to fence in a pasture along a straight highway. The pasture is to contain 500 sq ft of land and be rectangular. If the fencing along the highway is heavy duty and costs $3 per foot, while the material for the remaining three sides costs $2 per foot, find the dimensions of the pasture with the minimum fencing cost.
Click here to see answer by scott8148(6628) About Me 

Question 112514: A lidless box is constructed from a square peice of tin by cutting a 10cm square from each corner and bending up the sides for the box. If the volume of the box is 1200cm cubed, find the dimensions to the nearest tenth of a centimetre.
Click here to see answer by ankor@dixie-net.com(22740) About Me 

Question 112726: y=2x^2-(3x-5)
Click here to see answer by MathLover1(20849) About Me 

Question 112700: I had to solve a quadratic equation by factoring and I recived it back as incorect. I dont know what I did wrong...could someone please explain this to me and show the correct steps if possible. I did not get 2 solutions for x and I cant figure out how to do this.
Thanks so much.
3x^2+11x-20=0
3x^2+15x-4x-20=0
3x(x+15)-4(x+5)=0
(3x-4)(x+5=0)


Click here to see answer by jim_thompson5910(35256) About Me 
Question 112700: I had to solve a quadratic equation by factoring and I recived it back as incorect. I dont know what I did wrong...could someone please explain this to me and show the correct steps if possible. I did not get 2 solutions for x and I cant figure out how to do this.
Thanks so much.
3x^2+11x-20=0
3x^2+15x-4x-20=0
3x(x+15)-4(x+5)=0
(3x-4)(x+5=0)


Click here to see answer by MathLover1(20849) About Me 

Question 112866: how do I solve: x2-12x +4=0. Please help.
I have to use the quadratic formula, but don't know what it is

Click here to see answer by solver91311(24713) About Me 

Question 112557: 4z^2=9
Click here to see answer by ankor@dixie-net.com(22740) About Me 

Question 112881: Please help solve this problem for me thank you.
If f(x)=2x^-7x+3 find f(2), and find f(-3) please show detail work. Thank you again.

Click here to see answer by jim_thompson5910(35256) About Me 

Question 112883: Please help solve this problem for me I am having a hard time my instructor is not making it easy. Thank you
Solve 2x^-3x-2=0 using quadratic formula. show detail work. Thank you again

Click here to see answer by jim_thompson5910(35256) About Me 

Question 112941: Thank you so much for the answer earlier I really apprecate it. I have one final question of the day hope you can help me out. Thanks again
if a rock is thrown upward with an initial velocity of 64 feet per second from the top of a 25 foot building write the a) height(s) equation using this information typing hint:t^2
b) how high is the rock after 1 second, show work
c)after how many seconds will the graph reach maximum height, show work
d)what is maximum height, show work

If you can help me with this it will save my life thank you again.

Click here to see answer by bucky(2189) About Me 
Question 112941: Thank you so much for the answer earlier I really apprecate it. I have one final question of the day hope you can help me out. Thanks again
if a rock is thrown upward with an initial velocity of 64 feet per second from the top of a 25 foot building write the a) height(s) equation using this information typing hint:t^2
b) how high is the rock after 1 second, show work
c)after how many seconds will the graph reach maximum height, show work
d)what is maximum height, show work

If you can help me with this it will save my life thank you again.

Click here to see answer by solver91311(24713) About Me 

Question 112928: it's a word problem.
Nancy wants to buy a mat for a photographtaht measures 14 in by 20 in. She wants to have an even border around the picture when it is mounted on the mat. If the area of the mat is 352 in squared How wide will the border be? I know the anwser is 1 inch. I just don't see why.

Here's what I've tried.
A=LW
(14+x)squared (20+x)Squared
280+14x + 20x+xSquared
280+34x+xsquared=0
Since this can't be factored i subtracted the 280 from both sides and got
x2 +34x = -280
half of 34 is 17 and 17 times 17 is 136
So this becomes
x2 +34x + 136 = -144
(x-72)squared = -144
x-72 = sqare root of -144
x-72 = 12i
x=72+or-12i
but this doesn't equal 1 inch. Please help me

Click here to see answer by scott8148(6628) About Me 

Question 113094: 4x^= 13x + 12
Am I right by stating that there is no solution to this problem?

Click here to see answer by solver91311(24713) About Me 

Question 113289: the height in feet of a projectile after t seconds is given by h(t)=-16t^2 +96t
determine the values for which the projectile is at the ground.
(the -16 has an exponent of 2 I couldn't get it to show up right also I need to set this problem up as an equation the chapter we are working on has to do with factoring.)

Click here to see answer by SHUgrad05(58) About Me 
Question 113289: the height in feet of a projectile after t seconds is given by h(t)=-16t^2 +96t
determine the values for which the projectile is at the ground.
(the -16 has an exponent of 2 I couldn't get it to show up right also I need to set this problem up as an equation the chapter we are working on has to do with factoring.)

Click here to see answer by Earlsdon(6294) About Me 

Question 113291: A square is represented by 4x^2 +28x+49 inches squared. Find the length of a side of the square in terms of x
( I need to set this up in equation format and solve.)

Click here to see answer by Earlsdon(6294) About Me 
Question 113291: A square is represented by 4x^2 +28x+49 inches squared. Find the length of a side of the square in terms of x
( I need to set this up in equation format and solve.)

Click here to see answer by MathLover1(20849) About Me 

Question 113287: 4x -12y =5
-x +3y = -1
how do you solve this using the substitution method

Click here to see answer by MathLover1(20849) About Me 

Question 113295: The product of two odd Intergers is 143. Write an equation whose solution is one of the Intergers. Use Factoring to solve the equation and find both Intergers.
Click here to see answer by checkley71(8403) About Me 

Question 113519: An object is projected upward from the top of a tower. Its distance in feet above the ground after t seconds is given by s(t)=-16t+64t+80. How many seconds will it take to reach ground level?
Click here to see answer by stanbon(75887) About Me 

Question 113530: Fitting a quadratic model to data
Throughout the twentieth century, the eating habits of Americans changed noticeably .Americans started consuming less whole milk and butter and started consuming more skim and low fat milk and margarine. We also started eating more poultry and fish. In this project you will have the opportunity to investigate trends in per capita consumption of poultry during the twentieth century .
We will start by finding a quadratic model y=ax^2+bx+c that has ordered pair solutions that correspond to the data for US. Per capita consumption of poultry given in the table .To do so, substitute each data pair into the equation. Each time, the result is an equation in three unknown: a,b, and c. Because there are three pair of data, we can form a system of three linear equation equations in three unknowns .Solving for the values of a, b, and c gives a quadratic model that represents the given data.
US PER CAPITA CONSUMPTION OF POULTRY (IN POUNDS)
YEAR X POULTRY CONSUMPTION Y (IN POUNDS)
1909 9 11
1969 69 33
2001 101 66
Write the system of equations that must be solved to find the values of a, b, and c needed for a quadratic model of the given data.
Solve the system of equations for a, b c.
Write the quadratic model for the date. Note that the variable x represents the number of years after 1990.
In 1939 the actual U.S per capita consumption of poultry was 12 lbs per person. Based on this information, how accurate do you think this model is for years other than those given in the table?
Use your model to estimate per capita consumption of poultry in 1950.
According to the model, in what year was per capita consumption of poultry 50 pounds per person?
In what year was the per capita consumption of poultry at its lowest level? What was that level?

Click here to see answer by stanbon(75887) About Me 

Question 113411: I have a problem that is not from the textbook. My teacher has assigned the following problem and we are to use applications of the quadratic formula. I don't see how to put the problem into a square in order to use the quadratic formula. Here is the problem:
The rate of a bicyclist is 5mph faster than the rate of a runner. The bicyclist travels 12 miles in the same amount of time that it takes the runner to travel 8 miles. Find the rate of the runner.
This is how far I got:
12/x+5 = 8/x then, 8x - 12x +40 = 0
I would really appreciate any help. Thank you in advance.
Tynk

Click here to see answer by Fombitz(32388) About Me 

Question 113602: Use the quadratic formula to solve the equation
-
3x^2-40x=59

Click here to see answer by checkley71(8403) About Me 
Question 113602: Use the quadratic formula to solve the equation
-
3x^2-40x=59

Click here to see answer by stanbon(75887) About Me 

Question 113608: What values of b will make x^2 + bx + 2/5 a perfect square trinomial ?
Click here to see answer by checkley71(8403) About Me 
Question 113608: What values of b will make x^2 + bx + 2/5 a perfect square trinomial ?
Click here to see answer by stanbon(75887) About Me 

Question 113606: Solve the equation.

y 2 - 15 y + 44 = 0

Click here to see answer by checkley71(8403) About Me 

Question 113604: Two students solved a problem involving a quadratic equation. The first student made an error only in the constant term of the equation and determined the roots were 2 and 8. The second student made an error only in the coefficient of the linear term and determined the roots were -1 and -9. What was the quadratic equation ?
Click here to see answer by ankor@dixie-net.com(22740) About Me 

Question 113605: Write the equation x(x - 7) + 10 = 0 in quadratic form and then solve it by factoring.
Click here to see answer by checkley71(8403) About Me 

Question 113601:
The hypotenuse of a right triangle is 2.4 units long. The longer leg is 1.4 units longer than the shorter leg. Find the lengths of the sides of the triangle.

Click here to see answer by checkley71(8403) About Me 

Question 113254: Can you please help me with this equation? 2x-1= x^2-4x+4
Click here to see answer by ankor@dixie-net.com(22740) About Me 

Question 113620: Write three quadratic equations, with a, b, and c (coefficients of x2, x, and the constant) as:
Integers
Rational numbers
Irrational numbers

Click here to see answer by jim_thompson5910(35256) About Me 

Question 113683: Could someone please help me with this problem.
The product of two odd intergers is 143. Write an equation whose solution is one of the Intergers. Use factoring to solve the equation and find both intergers.

Click here to see answer by josmiceli(19441) About Me 

Question 113676: Could someone please help me with this problem.
A rectangular picture frame is 5 inches higher than it is wide and has an area of 126 square inches. Write an equation whose solution is the width of the picture frame. Use factoring to solve the equation and find the Dimensions of the frame.

Click here to see answer by josmiceli(19441) About Me 

Question 113700: Starting with ax2 + bx + c = 0 and show each step to end up with:
x = - b + √b2 - 4ac
_______________________
2a

Click here to see answer by MathLover1(20849) About Me 

Question 113716: Solve using the square root property:
(x + 8)2 = 81

Click here to see answer by jim_thompson5910(35256) About Me 

Question 113715: Solve using the square root property:
5x2 = 100

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Question 113718: Solve by using quadratic formula
4x^2-3x+3=0

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Question 113714: Solve by factoring:
x2 – 9x = -20

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Question 113726: Solve by completing the square:
x2 + 8x + 13 = 0

Click here to see answer by stanbon(75887) About Me 

Question 113729: Solve using the quadratic formula:
3x2 – 2x = 15x – 10

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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, 20341..20385, 20386..20430, 20431..20475, 20476..20520, 20521..20565, 20566..20610, 20611..20655, 20656..20700, 20701..20745, 20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975, 24976..25020, 25021..25065, 25066..25110, 25111..25155, 25156..25200, 25201..25245, 25246..25290, 25291..25335, 25336..25380, 25381..25425, 25426..25470, 25471..25515, 25516..25560, 25561..25605, 25606..25650, 25651..25695, 25696..25740, 25741..25785, 25786..25830, 25831..25875, 25876..25920, 25921..25965, 25966..26010, 26011..26055, 26056..26100, 26101..26145, 26146..26190, 26191..26235, 26236..26280, 26281..26325, 26326..26370, 26371..26415, 26416..26460, 26461..26505, 26506..26550, 26551..26595, 26596..26640, 26641..26685, 26686..26730, 26731..26775, 26776..26820, 26821..26865, 26866..26910, 26911..26955, 26956..27000, 27001..27045, 27046..27090, 27091..27135, 27136..27180, 27181..27225, 27226..27270, 27271..27315, 27316..27360, 27361..27405, 27406..27450, 27451..27495, 27496..27540, 27541..27585, 27586..27630, 27631..27675, 27676..27720, 27721..27765, 27766..27810, 27811..27855, 27856..27900, 27901..27945, 27946..27990, 27991..28035, 28036..28080, 28081..28125, 28126..28170, 28171..28215, 28216..28260, 28261..28305, 28306..28350, 28351..28395, 28396..28440, 28441..28485, 28486..28530, 28531..28575, 28576..28620, 28621..28665, 28666..28710, 28711..28755, 28756..28800, 28801..28845, 28846..28890, 28891..28935, 28936..28980, 28981..29025, 29026..29070, 29071..29115, 29116..29160, 29161..29205, 29206..29250, 29251..29295, 29296..29340, 29341..29385, 29386..29430, 29431..29475, 29476..29520, 29521..29565, 29566..29610, 29611..29655, 29656..29700, 29701..29745, 29746..29790, 29791..29835, 29836..29880, 29881..29925, 29926..29970, 29971..30015, 30016..30060, 30061..30105, 30106..30150, 30151..30195, 30196..30240