Tutors Answer Your Questions about Quadratic Equations (FREE)
Question 474815: I need a brush-up on completing the square. I am working with equations for ellipses. I just need help getting this problem into the right form for an ellipse by completing the square.
Here is an example:
x^2-2x+4y^2+8y+1=0
I know that eventually this ends up looking like (x^2-2x+1)+4(y^2+2y+1)=-1+1+4(1). I do not understand how we get here. I know that we are supposes to multiply both(?) sides by the square of half of the x coefficients, but I'm still confused. Anyway, an explanation for a dummy like me would be super awesome. Thanks!
Click here to see answer by Edwin McCravy(20054)   |
Question 474925: find three consecutive integers such that the square of the sum of the smaller two is equal to twice the largest.
(three consecutive integers are x, x+2, and x+4)
(the square of the smaller two are x^2 and (x+2)^2)
Click here to see answer by mananth(16946)  |
Question 474933: I have to figure the dimensions of a fence in a rectangular area, using a 1000 sq ft of my back yard for a dog to run and play in using a Quadratic Equation. Did I calculate this the width correct? Thank you
L = 2W +5
L = length, W = width, P = perimeter, A = area
〖2w〗^2+5w-1000 = 0
A=2, B=5, C=1000
W = (-b±√(b^2-4ac))/2a
W = (-5±√(5^2-4(2)-1000))/(2(2))
W=(-5±√(5^2-4(2)-1000))/(2(2))
W = (-5±√(25-992))/4
W = (-5±√967)/4
W = (-5±√(-5+241.75))/4 = (236.75)/4 = 59.19 OR (-5-241.75)/4 = (-236.75)/4 = -59.19
W = 59.19 yards of fence
Click here to see answer by mananth(16946) |
Question 475083: I am a little confused on this problem and not sure where to start. Help would be greatly apprieciated.
The polynomial 0.0014x^3-0.07x^2+1.5x+11 models natural gas consumption in trillions of cubic feet, where x=0 corresponds to 1960, x=1 to 1961, and so on. In which year between 1979 and 1990 was natural gas consumption about 21.7 trillion cubic feet?
Thanks Abby
Click here to see answer by ankor@dixie-net.com(22740)  |
Question 475232: Find the vertex and the line of symmetry of the quadratic function.
F(x)=-2x^2+2x+1
The x coordinate of the vertex is ____. (Type a simplified fraction.)
The y coordinate of the vertex is ____. (Type a simplified fraction.)
The equation line of symmetry is ____. (Type a simplified fraction.)
Click here to see answer by rfer(16322) |
Question 475389: Problem: Solve using the quadratic formula: 5x(squared)-2x+9=0
x= 2 times the square root of 2(squared)-4(5)(9) over 5(2).
x= 2 times the square root of 4-180 over 10.
x= 2 times +or- the square root of -176 over 10.
x= +or- the square root of -176 over 5.
That is as far as I've gotten in the problem. I know that the answer is supposed to be 1/5 +- 2(square root of 11)/5i. I'm having a difficult time figuring out how to get there from the last step of the problem I listed.
Thank you.
Click here to see answer by Alan3354(69443)  |
Question 475466: Can you please help me solve this word problem involving quadratic equations, I am lost and can't figure out where to start.
The function D(x) models the cumulative number of deaths from a disease x years after 1984, estimate the year when there were 100,000 deaths.
D(x) =2285x^2 + 5583x + 5540.
There were approximatley 100,000 in the year __________________
(round to the nearest year)
Your help will be appreciated!
Thanks Abby
Click here to see answer by Theo(13342)  |
Question 475756: What is the discriminant and how do you find it if you are given a quadratic equation? For instance, if you have -x² + 12 + 20 = 0, what would the discriminant be? How many solutions would this equation have?
Click here to see answer by rfer(16322) |
Question 475756: What is the discriminant and how do you find it if you are given a quadratic equation? For instance, if you have -x² + 12 + 20 = 0, what would the discriminant be? How many solutions would this equation have?
Click here to see answer by Gogonati(855)  |
Question 475787: Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour, and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. ( x=1 is the day tickets go on sale).
tickets=-0.26x squared+13x=35
1. Does the graph of this equation open up or down? How did you determine this?
Click here to see answer by ewatrrr(24785)  |
Question 475786: Suppose you are an event coordinator for a large performance theater. One of the hottest new Broadway musicals has started to tour, and your city is the first stop on the tour. You need to supply information about projected ticket sales to the box office manager. The box office manager uses this information to anticipate staffing needs until the tickets sell out. You provide the manager with a quadratic equation that models the expected number of ticket sales for each day x. ( x=1 is the day tickets go on sale).
tickets=-0.26x squared +13x+35
1. Does the graph of this equation open up or down? How did you determine this?
Click here to see answer by ewatrrr(24785) |
Question 475750: Tickets will sale but once it reaches that peak point the sales will start to decrease because anytime you have a coefficients with negatives such as in this equation we already know that it is going to descend at some point which again will start once it reaches a certain point.
Click here to see answer by richard1234(7193)  |
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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, 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