Questions on Algebra: Quadratic Equation answered by real tutors!

Tutors Answer Your Questions about Quadratic Equations (FREE)

Question 189423: Solve for x: x^2 + 7x + 4 = 0. If the solutions are complex numbers, then give your solutions in the usual a + bi form.
Click here to see answer by josmiceli(9662)

Question 189349: A farmer has 500 feet of fencing to use to make a rectangular garden. One side of the garden will be a barn, which requires no fencing. How should the pen be built in order to enclose the largest amount of area possible?
Give your answer by filling in the blanks in the following sentence: The farmer should build the pen ______ feet away from the barn, and ________ feet wide, for an area of _______ square feet

How do I solve this?
Click here to see answer by ankor@dixie-net.com(15642)

Question 189355: 8. a) Given only the vertices of a triangle, describe the steps you would take to decide whether the triangle is an right-angle triangle.
Thank you very much!!!
Click here to see answer by scott8148(6628)

Question 189532: What is the difference between y=-f(x) and y=f(-x)?
The text gives an explanation on page 580, but I don't know how it would look with an actual equation. I can certainly read that y=-f(x) reflects y=f(x) vertically across the x-axis, and y=f(-x) reflects horizontally across the y-axis.
What I'm having difficulty understanding is, for a quadratic equation ax^2+bx+c, does -f(x) make it -ax^2+bx+c, or does it make it -ax^2-bx-c?
What about f(-x)?
Click here to see answer by feliz1965(151)

Question 189563: trying to solve 4x^2+150x=3000
Click here to see answer by jim_thompson5910(28536)

Question 189595: Graph y is greater than or equal to -2x^2+2x+4.
I got as far as: x=-b/2a-2/2(-2)
I need help, please!

Click here to see answer by ankor@dixie-net.com(15642)

Question 189600: The bases of an arch are 60 feet apart. The arch has a height of 40 feet. Write a quadratic function to approximate the arch.
I worked it out to: y=-2/45(x-30)^2+40
Am I correct?

Click here to see answer by user_dude2008(1861)

Question 189346: Analytic Geometry
3. Determine the radius and the diameter of teh circle with the center at
(-4, 3) and a point (2, -5) on its circumference. Round the radius to the nearest tenth, if necessary.
Thank you very much!!!!
Click here to see answer by feliz1965(151)

Question 189656: Distance from a Point to a Line
4.Find the distance from A(-2,-2) to the line joining B(5,2) and C(-1,4), to the nearest hundredth.
Thanks alot!!!!
Click here to see answer by jim_thompson5910(28536)

Question 189660: Distance from a Point to a Line
9.Find the distance from the point q(-2,-2)to the line y=3.
Can you help me please..
Thank you very much!!
Click here to see answer by user_dude2008(1861)

Question 189659: Distance from a Point to a Line
8.Find the distance from the point P(3,5)to the line x=-2.
thank you!!!
Click here to see answer by user_dude2008(1861)

Question 189634: Equation of a Circle
7. The point (a, 8) lies on the circle defined by x^2+y^2=100.
a) Explain why there are two possible values for a. Find these values.
b) Use a graph to check that the points corresponding to both values for a are on the circle.
Thank you very much!!!!
Click here to see answer by Edwin McCravy(8884)

Question 189657: Distance from a Point to a Line
6.Find the exact distance from the point D(4,-2) to the line segment joining the points E(1,3) and F(-4,-2).

pleaseeee help me ...thank you very much!!
Click here to see answer by Alan3354(30990)

Question 189630: Equation of a Circle
6. Determine an equation for the circle that has a diameter with endpoints
A(-4, 3) and B(4, -3).
Thank you
Click here to see answer by Mathtut(3670)

Question 189635: Equation of a Circle
8. A farmer is building a circular corral to hold livestock. With distance measured in metres, the shape of the corral is modelled by the equation x^2+y^2=64.
a) Find the length of fencing required for this corral.
b) Find the area of the corral.
Thank you very much!!!
Click here to see answer by Mathtut(3670)

Question 189688: Equation of a Circle
6. Determine an equation for the circle that has a diameter with endpoints
A(-4, 3) and B(4, -3).
Thank you!!!!
Click here to see answer by jim_thompson5910(28536)

Question 189663: Distance from a Point to a Line
13.The equation of a circle with centre O(0,0)is x^2+y^2=10.The points P(1,3) and Q(-3,-1)are endpoints of chord PQ.Find the exact distance from the centre of the circle to the chord.
Thank you alot..
Click here to see answer by Edwin McCravy(8884)

Question 189841: Use the quadratic formula to solve 2y^2 - 6y - 8 = 0
Click here to see answer by jim_thompson5910(28536)

Question 189843: Equation of a Circle
11.a) State the radius of the circle given by the equation x^2+y^2=169
Thank you sooooo much!!!!
Click here to see answer by jim_thompson5910(28536)

Question 189849: 3. Find the shortest distance from the point P(-5, 9) to the line 3x-2y=6. Round to the nearest tenth if necessary.
Thank you very much!!!!!
Click here to see answer by solver91311(16872)

Question 189847: 12. Determine the equation of the line, in standard form (S.F.):
c) perpendicular to the x-axis and with the same x-intercept as 6x-5y+18=0.
Thank you very much!!!!
Click here to see answer by solver91311(16872)

Question 189862: Find the height, of a ball, above ground using the following information.
wait 2 seconds, velocity is 55 ft/sec, initial height above ground is 2 ft
Click here to see answer by Alan3354(30990)

Question 189880: Identify the value of a,b, and C in the functions
y=3x^2-5x+2
Click here to see answer by jim_thompson5910(28536)

Question 189904: Solve by completing the square.

y^2 - 12y = -11
Click here to see answer by nerdybill(6951)

Question 189904: Solve by completing the square.

y^2 - 12y = -11
Click here to see answer by jim_thompson5910(28536)

Question 189964: I am in need of assistance in creating an equation that describes the chart as follows
X Y
0 0
1 .5
2 2.0
3 4.5
4 8
5 12.5
I realize the progression of .5,1.5,2.5,4,4.5. I can't figure out the equatio

Click here to see answer by Alan3354(30990)

Question 189848: 2. For a line segment ST, one endpoint is S(-1/2), 4) and the midpoint is
M(6, -3/4).
Find the coordinates of the other endpoint T.
Thank you very much!!!!
Click here to see answer by edjones(7569)

Question 189971: Use the Completing the Square method to find the vertex form of the quadratic function y = x^2 + 7x + 12.
Click here to see answer by Mathtut(3670)

Question 189971: Use the Completing the Square method to find the vertex form of the quadratic function y = x^2 + 7x + 12.
Click here to see answer by nerdybill(6951)

Question 189970: Find the vertex of the parabola y = 3(x+1)^2 - 4. Give your answer by filling in the blanks in the following sentence, where the first blank is the coordinates of the vertex, and the second blank is either the word "highest" or the word "lowest".
The vertex is ______ , and this point is the _________ point on the parabola.
Click here to see answer by Mathtut(3670)

Question 189969: Use the discriminant to find how many places the quadratic function crosses the x-axis.
x^2 - 5x - 14 = 0

a) Two zeros
b) One zero
c) No zeros
Click here to see answer by Mathtut(3670)

Question 189968: Use the discriminant to find how many places the quadratic function crosses the x-axis.
4x^2 + 8x = 0

a) Two zeros
b) One zero
c) No zeros
Click here to see answer by stanbon(57272)

Question 190011: how do i do this question.....- + 30 = 50x*255x (*= exponent)
Are there any other websites that can help me with these problems??
Click here to see answer by Alan3354(30990)

Question 190025: what does it mean with the equal to 2/3 x+1?

Click here to see answer by Alan3354(30990)

Question 190057: Find the x-intercepts of the graph of the equation.......Please explain steps...
y=x^2+2x-35
x^2 is x squared.
Click here to see answer by solver91311(16872)

Question 190088: A community theater sells about 150 tickets to a play each week when it charges $20 per ticket. For each $1 decrease in price, about 10 more tickets per week are sold. The theater has fixed expenses of $1500 per week.
Write a model: write a verbal model and a quadratic function to represent the theater's weekly profit.
-----
What i did is this, but I am not sure if I am right:
y=(-x+20)(10x+150)-1500
y=-10x^2-150x+200x+3000-1500
y=-10x^2+50x+1500
I really don't understand how to create equations out of word problems like this. I really appreciate the help.. Thank You !
Click here to see answer by solver91311(16872)

Question 189988: 2. Choose the equation of the parabola with a vertex at the origin and a focus at (0, –3).
1. y=-1/3x
2. y=1/12x^2
3. y=-1/3x^2
4. y=1/12x^2

Click here to see answer by cutepiscean5(19)

Question 190141: I need to find the equation that goes with a series of plotted points. The points form what appears to be part of a parabola. The coordinates given are:
x y
32 6
48 14
64 24
80 38
96 55
112 75
The scenario relates to the speed of a car (x) and the braking distance at that speed (y). So presumably another coordinate can also be 0,0.
Given the staring coordinate of 0,0 I have worked out that in the formula form y = ax^2 + bx + c that c = 0, but I cannot work out the procedure to use to solve for a and b and come up with the equation. I have tried simultaneous equations but think I am doing something wrong. My boyfriend talked about solving it by taking logs but we have not been taught that way at school.
Thanks
Click here to see answer by stanbon(57272)

Question 190294: A signal flare is fired upward with initial speed 245m/s. A stationary balloonist at the height of 1960 m sees the flare pass on the way up. How long after this will the flare pass the balloonist again on the way down?
This is for my son, and yes, I'm a few years out of practice. He's tried setting it to zero with: -4.9t^2-245t+1960=0. I think h=rt-4.9t^2 is the formula was also given to him. Can you help, please? He knows the answer is 30 seconds, but can't show the work. Thanks
Click here to see answer by jim_thompson5910(28536)

Question 190301: What is the domain of f, range of f, vertex, axis of symmetry, x-intercept (s), y-intercept, determine whether it has a minimum or a maximum value and state that value for f(x)=x^2+x-2
PLZZZZ help me in STRUGGLING!
Click here to see answer by solver91311(16872)

Question 190232: How do you solve this problem? and I need answer too
Click here to see answer by Mathtut(3670)

Question 190316: Prove the identity : sin theta tan theta + cos theta= sec theta
Click here to see answer by stanbon(57272)

Question 190329: Please help me solve this equation 4y2 + 3y - 1 = 0

Click here to see answer by vleith(2825)

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