Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 1179238: A line has an equation of x + 5y - 4 = 0. If the line x - ky - 17 = 0 makes an angle of 45 degrees counter-clockwise from the line x + 5y - 4 = 0, find
the value of k.
Click here to see answer by mananth(16946)

Question 1179364: The function f(t) = - 4.92t ^ 2 + 17.69t + 575 is used to model the height of an object being tossed from a tall building where h () is the height in meters and tis the time in seconds . What are the domain and range ? Round to the nearest hundredth
Click here to see answer by Boreal(15235)

Question 1179404: Suppose r and s are the roots of the quadratic equation 3x^2 + 2x - 8 = 0.
Find the following values.
a. r + s
b. rs

Click here to see answer by ikleyn(52747)

Question 1179405: Suppose r and s are the roots of the quadratic equation 3x^2 + 2x - 8 = 0.
Find the following values.
a. the average of r and s
Click here to see answer by ikleyn(52747)

Question 1179529: How many solutions does x² - 4x + 4 =0 have?
Click here to see answer by mananth(16946)

Question 1179527: Find the values of k such that x² + 6x + k = 0 will have exactly two solutions.
x² + 6x + k = 0

Click here to see answer by MathLover1(20849)

Question 1179530: If the consumer's income rises to $60, then the budget line for hot wings and beer would
Click here to see answer by MathLover1(20849)

Question 1179755: Find a quadratic function that has a minimum value of -14.
Click here to see answer by MathLover1(20849)

Question 1179756: The graph of a quadratic function passes through (-2, 4) and has
vertex (1, -6).
Use symmetry to identify one other point that must be on the
graph of this function.
Click here to see answer by ewatrrr(24785)

Question 1179754: Use the function f(x)= 4x^2 + 4x - 15.
Find the value of x that gives the minimum. For parts (b) - (d), refer to
this number as m.
b. Calculate f(m 1 1) and f(m 2 1).
Click here to see answer by MathLover1(20849)

Question 1179834: The graph of a quadratic function passes through the origin and has
vertex (4, 16).
Use symmetry to identify one other point that must be on the graph of
this function.
Find an equation for this function.
Click here to see answer by MathLover1(20849)

Question 1179958: A quadratic function has zeros 3 and 9. It passes through point (6, 11).
What is the vertex of the graph?
Click here to see answer by josgarithmetic(39613)

Question 1179958: A quadratic function has zeros 3 and 9. It passes through point (6, 11).
What is the vertex of the graph?
Click here to see answer by MathLover1(20849)

Question 1179958: A quadratic function has zeros 3 and 9. It passes through point (6, 11).
What is the vertex of the graph?
Click here to see answer by greenestamps(13195)

Question 1179959: The line of symmetry for y= x^2 + 16x + 60 is x= -8. Find the equations
of three different quadratics that also have x= -8 as the line of
symmetry. Make sure that each equation has a different value of a.
Click here to see answer by MathLover1(20849)

Question 1179956: Two numbers have a sum of 36.
Write an equation for the product of the two numbers.
Use roots to explain why the maximum product must occur when the
two numbers are both 18.
Click here to see answer by MathLover1(20849)

Question 1179997: Aaron works two times as fast as Michael. Aaron can finish a job in 1 hour. If Aaron and Michael are working together, how long will it take them to finish the job?
Click here to see answer by josgarithmetic(39613)

Question 1179821: Determine the domain and range of {(x,y)|y=√ x2-49}
Click here to see answer by MathLover1(20849)

Question 1180025: Thirteen less than three times a number x is forty-seven
Click here to see answer by ankor@dixie-net.com(22740)

Question 1180054: What number should be added to the equation 2 x squared plus 8 x minus 5 equals 0 if you will use completing the square?

Click here to see answer by MathLover1(20849)

Question 1180054: What number should be added to the equation 2 x squared plus 8 x minus 5 equals 0 if you will use completing the square?

Click here to see answer by mananth(16946)

Question 1180054: What number should be added to the equation 2 x squared plus 8 x minus 5 equals 0 if you will use completing the square?

Click here to see answer by greenestamps(13195)

Question 1180054: What number should be added to the equation 2 x squared plus 8 x minus 5 equals 0 if you will use completing the square?

Click here to see answer by ikleyn(52747)

Question 1180054: What number should be added to the equation 2 x squared plus 8 x minus 5 equals 0 if you will use completing the square?

Click here to see answer by MathTherapy(10549)

Question 1180183: Henry throws a tennis ball over his house. The ball is 6 feet above the ground when he lets it go. The quadratic function that models the height, in feet, of the ball after t seconds is mc003-1.jpg. How long does it take for the ball to hit the ground?
Click here to see answer by mananth(16946)

Question 1180202: the sum of the two numbers is -3, while their product - 56. What are those numbers
thank you
Click here to see answer by Boreal(15235)

Question 1180203: the sum of the squares of two consecutive numbers is 61.What are those numbers
Click here to see answer by Boreal(15235)

Question 1180203: the sum of the squares of two consecutive numbers is 61.What are those numbers
Click here to see answer by mananth(16946)

Question 1180250: Consider the quadratic equation y=9 x^2 - 8 x.
Complete the square to express the quadratic in standard form y=a (x-h)^2 +k.
a=
h =
k =
Click here to see answer by MathLover1(20849)

Question 1180263: Consider the quadratic equation y=x^2+8 x + 18.
Complete the square to express the quadratic in standard form y=a (x-h)^2 +k
a=
h =
k =

Click here to see answer by MathLover1(20849)

Question 1180271: Convert each of the following expressions to fully factored form. Prove each solution by expanding and simplifying the factored form, or by representing the solution using Polynomial Tiles.
x2 - 9x + 14
16y2 - 25
6z2 + 5z - 4
w2 + 8w + 16
3p2 + 3p - 6
Click here to see answer by MathLover1(20849)

Question 1180267: Consider the quadratic equation y=-10 x^2 - 60 x + 8.
Complete the square to express the quadratic in standard form y=a (x-h)^2 +k.
a=
h=
k =
Click here to see answer by josgarithmetic(39613)

Question 1180254: Consider the quadratic equation y=x^2+8 x + 18.
Complete the square to express the quadratic in standard form y=a (x-h)^2 +k
a=
h =
k =
Click here to see answer by josgarithmetic(39613)

Question 1180273: Hello i need help with this question thank you so much for your help and please show the answers as clear as possible.

A clay pigeon is fired into the air. It moves along a path according to the equation h(x)=-5x^2++14x. h(x) represents the height the pigeon travels above ground, and x represents the horizontal distance. A person fires a bullet which goes in a straight line according to the formula b(x)=0.5x+3.25.x is still the horizontal distance, along the ground. Distances are in metres.
It is possible that the bullet can hit the clay pigeon in two places along h(x), depending on when the person fired the rifle. What are those two places (answer in terms of horizontal distance and height above ground)? All numbers should be accurate to the nearest tenth.
A helpful formula is the quadratic formula -b±√b^2-4ac/2a

for quadratics of the form: ax2+bx+c=0.

Click here to see answer by Boreal(15235)

Question 1180370: Use the quadratic formula to determine, accurate to one decimal place, the roots, if they exist, for each quadratic relation.
y = 2x2 +
y = x2 -
y = x2 +
y = - 9x2 -
Click here to see answer by ikleyn(52747)

Question 1180371: Rewrite each of the following in vertex form by completing the square:
y = x2 - . . .
y = x2 + . .

y = 4x2 + . . .
Click here to see answer by ikleyn(52747)

Question 1180372: Expand and simplify the following-
a). (3x-1)^2
b). (x-2)^2
c). 3(2x-3)^3
d). (4x+y)(2x-y)
e). (3x-2)(2x+1)-(x-3)^2
Click here to see answer by ikleyn(52747)

Question 1180372: Expand and simplify the following-
a). (3x-1)^2
b). (x-2)^2
c). 3(2x-3)^3
d). (4x+y)(2x-y)
e). (3x-2)(2x+1)-(x-3)^2
Click here to see answer by MathLover1(20849)

Question 1180374:
Click here to see answer by ikleyn(52747)

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