Questions on Algebra: Quadratic Equation answered by real tutors!

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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 ikleyn(52778)

Question 1180466: A rectangular chicken yard was built against an existing
shed wall. 30 m of fencing was used to enclose 108 m2.
Find the dimensions of the yard.

Click here to see answer by ikleyn(52778)

Question 1180467: Expand and simplify the following:
f) 5(3x^2+1)(x^2-1)
g) (4x+3)^2-3(2x+3)(2x-3)
h) (2x^2+3x-1)(3x^2-x+3)

Click here to see answer by ikleyn(52778)

Question 1180508: Please help me in this equation
Click here to see answer by josgarithmetic(39617)

Question 1180533: Determine the x-intercept and vertex for this equation:
y = (x - 3)(x + 5)
*can work be shown please for understanding
Click here to see answer by ikleyn(52778)

Question 1180546: Use the quadratic formula to determine, accurate to one decimal place, the roots, if they exist, for each quadratic relation.
a) y = 2x2 + 3x + 1
b) y = x2 - 3x + 5
c) y = x2 + x - 5
d) y = - 9x2 - 6x + 1
Click here to see answer by mananth(16946)

Question 1180559: Write an equation of the polynomial, in standard form, with roots 3,-5,2 that also pass through the point (4,54).
Click here to see answer by greenestamps(13200)

Question 1180559: Write an equation of the polynomial, in standard form, with roots 3,-5,2 that also pass through the point (4,54).
Click here to see answer by MathLover1(20849)

Question 1180624: 1.You have a function f(x)=x+2 Show what happens to the right-hand expression with f(x^2-11), in factored form
Click here to see answer by josgarithmetic(39617)

Question 1180659: Write a quadratic equation in the form of ax^2 + bx + c = 0 that has 2 - i as a solution
Click here to see answer by josgarithmetic(39617)

Question 1180909: ргрг https://www.stepcalculator.com/integral-calculator.html
Click here to see answer by math_helper(2461)

Question 1180945: Solve the following quadratic equations. (They are unfactorable)

x2+9x+3
x2+-2x-11

Click here to see answer by josgarithmetic(39617)

Question 1180945: Solve the following quadratic equations. (They are unfactorable)

x2+9x+3
x2+-2x-11

Click here to see answer by ikleyn(52778)

Question 1180951: The graph of y=ax^2+bx+c passes through the points (0,-9) and (-1,9). Given that the equation of asymmetry is x=4, find the values of a, b, and c.
Click here to see answer by greenestamps(13200)

Question 1181007: A picture frame is 30 cm by 24 cm. There are 520 cm^2 of picture showing. Find the width of the frame.
Click here to see answer by josgarithmetic(39617)

Question 1181081:
Click here to see answer by ikleyn(52778)

Question 1181060: Given the following information, determine the equation of the quadratic relation. a) compressed by a factor of 12, opens down and has it's vertex at (4,2)
b) stretched by factor of 3 with a minimum value of 5 and the axis of symmetry at X=1
Click here to see answer by greenestamps(13200)

Question 1181132: A ball leaves the end of a baseball bat and travels according to the formula h(t) = -16t² + 64t where h is the height of the ball in feet and t is the time in seconds. How many seconds will it take for the ball to reach a height of 64ft in the air?

Click here to see answer by ikleyn(52778)

Question 1181245: A book collector bought a first edition of " The Picture of Dorian Grey" by Oscar Wilde at auction for $1500. This book increases in value at a rate of 13% per year.At the same auction, the collector bought a copy of "Pride and Prejudice" by Jane Austen for $1800. This one increases in value at a rate of 9% per year. Create an exponential function for each situation and use the functions to algebraically determine the amount of time it would take for the twobooks to be equal in value.
I appreciate any help :)
Click here to see answer by ikleyn(52778)

Question 1181249: Verify the trigonnometric identity (cscx/2cosx) = )1/sin2x)
Thank you for any help.
Click here to see answer by ikleyn(52778)

Question 1181264: The line of symmetry for the quadratic equation y = ax2 + 8x - 3 is x = 4. What is the value of "a"?

Click here to see answer by josgarithmetic(39617)

Question 1181264: The line of symmetry for the quadratic equation y = ax2 + 8x - 3 is x = 4. What is the value of "a"?

Click here to see answer by ikleyn(52778)

Question 1181266: Help with Quadratic Equation please
Use the quadratic formula to solve for x.

Round your answer to the nearest hundredth.
If there is more than one solution, separate them with commas.
Click here to see answer by MathLover1(20849)

Question 1181246: Alggebraically determine the x-intercepts and y-intercepts and sketch the graph of the polynomial : P(x) = 2x^3 -9x^2 +7x +6
Thank you for any help.
Click here to see answer by josgarithmetic(39617)

Question 1181248: Determine ALL solutions, in radian measure, for the equation

Click here to see answer by Edwin McCravy(20054)

Question 1181274: Ella throws a hockey puck up at a rate of 20 ft/sec from a height of 5 feet.
How long will it take for the hockey puck to hit her on the head if Ella is 5.5 ft tall?
I solved it and got 0.026 and 1.23 as the answers (rounded), but I don't know which one is the correct answer.
Also I used the equation . a is 32.
Click here to see answer by ikleyn(52778)

Question 1181247: The graph of y= f(x) with points A( -8,-1), B ( -6,-4) , and C (4,-4) is transformed to give the image points A'( -6,-3), B' ( -5,6) and C'( 0,6) . Plot the points and determine the equation of the image function in the form
y=af[b(x-c)) +d.
I appreciate any help.
Click here to see answer by greenestamps(13200)

Question 1181309: two groups are visiting a museum the first group includes four adults and 20 students they paid $82 for their tickets the second group includes six adults and 22 students and they play $99 for their tickets what is the cost of an adult ticket what is the cost of a student ticket
Click here to see answer by josgarithmetic(39617)

Question 1181359: The diagram show a square - shaped lawn with 6 m by 8 m pool built inside.
A) Find an equation expressing the area of the lawn in terms of the side length, x, of the shape.
B) State its domain and range.
Click here to see answer by josgarithmetic(39617)

Question 1181358: the coordinates of two point on a parabola are (7, 4) and (4, 3). Another point on the parabola is (8, 24). find the equation of the parabola F(x) = a(x-h)^2 + k.
Click here to see answer by MathLover1(20849)

Question 1181357: the coordinates of two point on a parabola are (7, 4) and (4, 3). Another point on the parabola is (8, 24). find the equation of the parabola F(x) = a(x-h)^2 + k.
Click here to see answer by ikleyn(52778)

Question 1181355: The diagram shows a suspension bridge with a center span of 4200 ft. and a tower height of
500 ft. with the lowest part of the suspender 10 ft. above the base of the bridge. Write an
equation to represent the curve of the suspender with h, the tower height from the base of the
bridge, in ft. as a function of d, the horizontal distance from the center of the bridge, in ft.,
assuming that the suspender is symmetrical in shape.

Click here to see answer by greenestamps(13200)

Question 1181407: Write the equation of each quadratic relation in vertex form for a parabola that has a vertex of (1,1) and
passes through the point (2, -1) and passes through the point.
Click here to see answer by josgarithmetic(39617)

Question 1181411: Choose one of the following (circle your choice); determine the equations and solve the problem below.
(Remember to define variables, include a diagram or sketch and interpret your answers in relation to the problem).
A) A farmer is constructing a pig pen and is using his barn wall as one side of the pen. If he has 32 m of fencing and wants to use it all, determine the dimensions that will produce the maximum area of the pen.
Click here to see answer by ikleyn(52778)

Question 1181410: A video tracking device recorded the height, h, in metres, of a baseball after it was hit. The data collected can be modeled by the relation: h = -5(t-2)2 +21, where t is the time seconds after the ball was hit.
a) What was the maximum height of the baseball and when was this height reached?

Click here to see answer by Solver92311(821)

Question 1181542: Determine ALL solutions , in radian measure , for the equation:
sin ( 1/2 ( theta - (pi/2)) = - (root3) /2
I know sine is negative in quadrants 3 and 4, but I am having real trouble understanding.
I appreciate any help. Thank you.
Click here to see answer by ikleyn(52778)

Question 1181562: A volcano ejected with an initial velocity of 304 feet per second. The height in feet is given by the equation H=-16t^2+ 304t where t is the time in seconds. We will use the equation that traces the path of the projectile to determine the following information:
1) The time it takes the projectile to reach its maximum height (using the vertex formula: t=-b/2a)
2) The maximum height of the projectile (use the result from part 1 to find the maximum height of the projectile)
3) Find the time it takes the projectile to return to the ground. Assume that the projectile starts at height H=0.
Solve by factoring to find the time it takes the projectile to return to the ground.
Show all work and explain all steps
Click here to see answer by ankor@dixie-net.com(22740)

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