Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 46964: For the function y = x2 - 6x + 8, perform the following tasks:
a) Put the function in the form y = a(x - h)2 + k.
Answer:
Show work in this space.

b) What is the line of symmetry?
Answer:

c) Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x - h) 2 + k.
Show graph here.

Explanation of graphing.

d) In your own words, describe how this graph compares to the graph of y = x2?
Answer:

Click here to see answer by Nate(3500)

Question 46965: Explain what the value of the discriminant means to the graph of y = ax2 + bx + c. Hint: Chose values of a, b and c to create a particular discriminant. Then, graph the corresponding equation
Click here to see answer by Nate(3500)

Question 47097: the answer is 9.8 and 1.2 how did it happen?
a^2-11a=12=o
=11-sqrt73/2 or 11+sprt73/2 ????????????? sqrt 73 is not an integer
Thank you
Click here to see answer by Earlsdon(6294)

Question 47373: Solve the following quadratic equations by factoring or by any of the techniques.
4x^2 - 8x + 3 =5
Thanks
Click here to see answer by beccap528(1)

Question 47371: Solve the following quadratic equations by factoring or by any of the techniques
x^2 - 9x - 4 =6

Thanks
Click here to see answer by checkley71(8403)

Question 47370: Solve the following quadratic equations by factoring or by any of the techniques.
(x-1)^2 = 7
Thanks
Click here to see answer by Nate(3500)

Question 47426: Construction. A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft^2, what is the width of the path?
Thanks:)
Click here to see answer by checkley71(8403)

Question 47489: Let f(x)=x^3-8x^2+17x-9. Use the factor theorem to find other solutions to
f(x)-f(1)=0, besides x=1.
Click here to see answer by stanbon(75887)

Question 47511: A skin heals according to N(t)+N(o)e^-0.02t, where N is the number of square centimeters of unhealed skin t days after an injury, and N(o) is the number of square centimeter covered by the original wound. How many days (to the nearest tenth ofa day) will it take for 50% of the wound to heal?
Click here to see answer by stanbon(75887)

Question 47398: This is for an exam. I need some help on Solving a quadratic equation with imaginary roots. Find all real or imaginary roots of:
3x^2+4x+4=0

As an example a similar problem: x^2+4x+5=0 had a solution of: x= -2+i or -2-i

Thanks
Click here to see answer by stanbon(75887)

Question 47512: Find the balance (to the nearest cent) if 24, 000 is invested at an annual interest rate of 6.8% for 10 years, compounded continuously.
Click here to see answer by stanbon(75887)

Question 47557: Solve for x (Hint: Factor the left-hand side)

x^2 + 4x + 4 =7

Thank You!!!
Click here to see answer by stanbon(75887)

Question 47482: The height, in feet, of a rocket t secods after blast-off is given by a formula h=1260t-16t^2. After how many seconds will the rocket first reach a height of 23,400 feet?
Click here to see answer by checkley71(8403)

Question 47465: I have to solve the following where "y" is a real number, and give one or both solutions if there are 2. Then simplify my answer(s) as much as possible.
(y-8)^2-32= 0

Thanks
Click here to see answer by checkley71(8403)

Question 47739: Identify the axis of symmetry, create a suitable
table of values, and sketch the graph (including the axis of symmetry).

y = -x^2 + 6x - 2
Thank You!
Click here to see answer by venugopalramana(3286)

Question 47738: Identify the axis of symmetry, create a suitable
table of values, and sketch the graph (including the axis of symmetry).
y = x^2 - 5x + 3
Thank You!
Click here to see answer by venugopalramana(3286)

Question 47783: Find all real or imaginary solutions to each equation. Use the method of your choice.

w^2 = -225

Thanks.

Click here to see answer by checkley71(8403)

Question 47789: i need help with this quadratic using the formula.. i did the work and my answer came out to be irrational is this true?
a=3x^2+
b=8x+
c=2
Click here to see answer by stanbon(75887)

Question 47912: Are these following trinomials a perfect square x^2 -2x + 1 and x^2 + 4x - 4

Thank You!

Click here to see answer by Nate(3500)

Question 47910: Solve by completing the square
x^2 = 5x + 2

Thanks
Click here to see answer by Nate(3500)

Question 47909: Solve by using the quadratic formula
x^2= 3x + 12

Thanks!
Click here to see answer by 1980.vikas(7)

Question 47943: Find the x - intercepts
y = x^2 + 2x - 8
Thank You!
Click here to see answer by smath(6)

Question 47948: Find the x intercepts

y = x^2 - 5x - 10

Thank you:)
Click here to see answer by checkley71(8403)

Question 47975: A 5.6 feet tall woman is shooting a free throw. The path of the basketball is parabolic in shape and the ball reaches its maximum height of 11.5 feet when the ball is 10 feet from the player. (i) Find the equation for the path of the ball. Let x be the horizontal distance from the shooter, and y be the height of the ball. (ii) the ball hits the front of the rim, which is 10 feet high. How far is the shooter from the rim?

Click here to see answer by stanbon(75887)

Question 47940: Find the constant term that should be added to make the following expressions a perfect- square trinomial

x^2 + 3x
and
x^2 + 8x
Thank You
Click here to see answer by checkley71(8403)

Question 48102: A 12 foot ladder is leaning against a wall. If the ladder reaches 8 feet high on the wall, what is the angle the ladder forms with the ground to the nearest degree?
Click here to see answer by tutorcecilia(2152)

Question 48139: how do u slove -b + square root b to the second power subtract 4ac over 2a to slove n to the second power subtract 8n-4=0? using the quadratic formula step by step??
Click here to see answer by stanbon(75887)

Question 48134: Solve

x^2 - 80 = 0
Thank You!

Click here to see answer by stanbon(75887)

Question 48134: Solve

x^2 - 80 = 0
Thank You!

Click here to see answer by Earlsdon(6294)

Question 48233: Henry invested $12,000.00 in a new resturant. When the resturant was sold two years later, he received $27,000.00. Find his average annual return by solving the equation 12,000.00(1+r)^2=27,000.00
Click here to see answer by atif.muhammad(135)

Question 48251: A ball is projected upward from the ground. Its distance in feet from the ground in t seconds is given by s(t)= -16t + 208t. At what times will the rocket be 550 feet from the ground?
Click here to see answer by tutorcecilia(2152)

Question 48198: Time to Swing:
The period T (time in seconds for one complete cycle) of a simple pendulum is related to the L (in feet) of teh pendulum by the formula 8T^2=pie^2L. If a child is on a swing with a 10-foot chain, then how long does it take to complete one cycle of the swing.
This problem is really throwing me off and it has a lot to do with the "pie." Any suggestions?
Click here to see answer by stanbon(75887)

Question 48257: If an object on Earth is propelled upward with an initial velocity of 32 ft. per second, then its height is given by h=32t-16t^2. After how many seconds does it reach its mamimum height?
Click here to see answer by Earlsdon(6294)

Question 48259: Alice wants to buy a mat for a photograph that 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 she chooses is 352 in.squared, how wide will the border be?
Click here to see answer by checkley71(8403)

Question 48318: Given a table of x and F(x) values how would you find the quadratic equation that describes it?
x -4, -3, -2, -1, 0
y -1, 0, 3, 8, 15
Since when x=0, y=15; I know that the constant term in the quadratic equation must be 15. Also I know that one of the roots is -3 because when y=0, x=-3. Additionally I have found that the second difference beteen the "y" values is always +2. (pattern of change is 2). I however, do not know how to use this piece of information to solve the problem. I have to write the quadratic equation that describes the relationship. I know that the relationship is quadratic because the second difference is a constant term - 2. Please help. Thank you for your time and help.
Click here to see answer by longjonsilver(2297)

Question 48345: apply the quadratic formula to find the roots of the given function, and then graph the function.
g(x) = x2 - x - 12
Click here to see answer by Nate(3500)

Question 48346: use the discriminant to determine the number of solutions of the quadratic equation, and whether the solutions are real or complex. Note: It is not necessary to find the roots; just determine the number and types of solutions.
x2 + 6x - 7 = 0
z2 + z + 1 = 0
(3)1/2y2 - 4y - 7(3)1/2 = 0
2x2 - 10x + 25 = 0
2x2 - 6x + 5 = 0
Click here to see answer by venugopalramana(3286)

Question 48344: apply the quadratic formula to find the roots of the given function, and then graph the function.
f(x) = x2 - 4
Click here to see answer by stanbon(75887)

Question 48344: apply the quadratic formula to find the roots of the given function, and then graph the function.
f(x) = x2 - 4
Click here to see answer by venugopalramana(3286)

Question 48343: complete the square, and find the roots of the quadratic equation.
x^2 + 16x = 0

Click here to see answer by venugopalramana(3286)

Question 48343: complete the square, and find the roots of the quadratic equation.
x^2 + 16x = 0

Click here to see answer by stanbon(75887)

Question 48280: Find two consecutive positive integers such that the sum of
their squares is 85.
Click here to see answer by Nate(3500)

Question 48550: How many solutions exist for a quadratic equation? Explain.

How do we determine whether the solutions are real or complex?

Click here to see answer by Nate(3500)

Question 48549: What three techniques can be used to solve a quadratic equation? Demonstrate these techniques on the equation "12x^2 - 10x - 42 = 0".
Click here to see answer by Nate(3500)

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