How do you put (x+3)^2-6 into the equation f(x)=ax^2+bx+c?
924177
FOIL out the first part of the expression and simplify:\n\n(x+3)^2 = x^2+6x+9\n\nTherefore, (x+3)^2-6 = x^2+6x+9-6 = x^2+6x+3\n\nTherefore using the general form, ax^2+bx+c, you can conclude that,\n\na=1, b=6, c=3\n\n----------------\n\nHope this helps
374296
First, simplify [a(b+c)=ab+ac]\n +8x -8 +3x = -8x\nSecond, combine like terms on each side [ax+bx=(a+b)x]\n +11x - 8 = -8x\nThird, isolate a variable [if a=b, then a+c = b+c]\n 19x - 8 = 0\n 19x = 8\nFourth, eliminate coefficient [if a=b, c =/= 0; a/c = b/c]\n x = 8/19\nFinally, evaluate.\n 8([8/19]-1) + 3(8/19) = -8(8/19)\n 8(-11/19) + (24/19) = -64/19\n -88/19 + 24/19 = -64/19\n True
618071
simplify to f(x)=(sqrt(x-2)(x-3))/(x-4)(x+5)\nthen sub in 1/x\nto get (sqrt(1/x -2)(1/x -3))/(1/x -4)(1/x +5)
798499
Given ax² + bx + c = 0, the quadratic formula tells us that:\n\nx = [ -b ± √(b²-4ac) ] ÷ 2a\n\nIn your problem, a=3, b=12, c=1  --  simply plug these values into the quadratic formula to solve for x.
1172065
if it is a quadratic (ax^2 + bx + c) then put it into the quadratic equation. that automatically will give you 0, 1, or 2 real answers. the equation is: x = [-b +/- (square root of b^2 - 4*a*c)] / 2a\n\nif (b^2 - 4*a*c) is negative, you have no real solutions. if it is zero, you have one real solution. if it is positive, you have 2 real solutions.\n\nthen, if for example you get  x=4 and x= -2, your factors are (x-4) and (x+2)
741312
If f(t)=(t-a)*(t-b) = t^2-(a+b)*t+ab; then \nI=(1/3)*t^3 - (a/2+b/2)*t^2 + a*b*t+C
32760
You can use the AC Method to answer this question:\n\nFirst, rewrite the expression so it's in the form Ax^2 + Bx + C where A,B, and C are constants (numbers)\n\n16x^2 + 8x - 15\n\nThere's no common factors we could take out first, so...\n\nMultiply A x C, which in this case is 16 x -15 or -240.  Then look for factors of this number that add up to B.  You're looking for two numbers that fill in the blanks below:\n__ x __ = -240\n__ + __ = 8\n\nPrime facorization will help give you some ideas, or make an ordered list of numbers that multiply to -240.  \n240 and -1\n120 and -2\n80 and -3\n60 and -4\n48 and -5\n40 and -6\n30 and -8\n24 and -10\n20 and -12\n\nSee how the last pair of numbers satisfies the conditions?\n\nRewrite your polynomial, substituting the 2 values in for B to have 4 terms:\n\n16x^2 + 20x - 12x -15\n\nThen factor by grouping\n(16x^2 - 12x) + (20x - 15)\n4x (4x - 3) + 5 (4x - 3)\n(4x + 5)(4x - 3)\n\nThis method works for most polynomials of the form Ax^2 + By + C!  \n\nYou can check your answer of (4x + 5)(4x - 3) by using the FOIL method and see that it does work.\n\nGood luck!
239087
We can use the quadratic formula :\n\nx = -6 +/- sqrt(36 - 4(3)(-3))\n-----------------------------\n2(3)\n\nx = -6 +/- sqrt(36 + 36)\n-----------------------\n6\n\nx = -6 +/- sqrt(72)\n-------------\n6\n\nx = -6 +/- 6sqrt(2)\n-----------------\n6\n\nx = -1 +/- sqrt(2)\n\nANSWER : x = -1 + sqrt(2) or\nx = -1 - sqrt(2)
617358
x = (-b +- sqrt(b^2-4ac))/(2a)\n\nThis equation solves the quadratic equation, where\n\nax^2 + bx + c = 0.
843483
using (x+y)^3 = x^3+3x^2y+3xy^2+y^3\n\nwe get (2a+b)^3 = 8a^3+12a^2b+6ab+b^3\n\n(ab+c)^3 = a^3b^3+3a^2b^2c+3abc^2 + c^3\n\n(6ab-c)^3 = 216a^3b^3-108a^2b^2c+18 abc^2 - c^3
672754
Take out the five so you have:\nx^2 + 8 + 16\nthen you can change that to\n(x + 4)^2 b/c you have to find a number that is the product of the a and c and the sum of b\nwhere you have: ax^2 + bx + c
708317
Ok, so if I have this correctly ... f(x) = 3x + 7 and you want to figure out the value of 2f(x²) - 5.\n\nSo first, you have to substitute x² into your equation for f(x) to obtain:\n3x² + 7.\n\nNow, this is the value for f(x²), so we can substitute it into the sexond equation:\n\n2f(x²) - 5\n=2(3x² + 7) - 5\n\nNow just expand and simplify.\n\n2(3x² + 7) - 5\n=6x² + 14 - 5\n=6x² + 9\n= 3(2x² + 3)
830875
You have an equation in the form of y = ax^2 + bx + c, and you want the form (y - k) = a(x - h)^2\nManipulating all those decimals can be very confusing, so let's try manipulating letters, instead.\na = -4.97\nb + 10.91\nc = -5.16\ny = a(x^2 + (b/a)x) + c\ny = a(x^2 + (b/a)x + (b/2a)^2x^2 - (b/2a)^2) + c\ny = a(x^2 + (b/a)x + (b/2a)^2x^2) - a(b/2a)^2 + c\ny + a(b/2a)^2 - c = a(2 + (b/2a))^2\ny + (b^2/4a) - c = a(x + (b/2a))^2\n(y + (b^2 - 4ac)/4a) = a(x + (b/2a))^2\nNow, substituting the numbers back in:\n(y +((10.91)^2  -4(-4.97)(-5.16))/(4(-4.97) = -4.97(x + (10.91/(2(-4.97))^2\n(y + (119.0281 - 102.5808)/-19.88) = -4.97(x + (10.91/-9.94))^2\n(y -16.4473/19.88) = -4.97(x - (10.91/9.94))^2\n(y - 0.82733) ≈ -4.97(x - 1.0976)^2
561262
u jammed the equation together.\ndo u mean\n6x^3 + ( 6/x - 2 * x^2 - x/3x2 - 3x + 3)\nits really hard to see ur question. can u write it out with spaces...\nhurry up i am waiting... lol
922434
There is only one step. Take the quadratic formula and plug in the numbers.\n\nIf ax^2 + bx + c = 0,\nx = (-b +/- sqrt(b^2-4ac))/2a\n\nFor the equation you gave, a=1, b=19, c=88. Plug those numbers in and see what you get.\n\nIf you're confused by the +/-, it's shorthand for writing two things in one. There are usually two values of x that work, one with + and one with -.
888899
f(x) = x^2 + 3x\n\nf(2-a) = (2-a)^2 + 3(2-a)\n\nExpand (2-a)^2 to (2-a)(2-a) and distribute the 3(2-a)\n\nf(2-a) = (2-a)(2-a) + 6 - 3a\n\nf(2-a) = 4 -2a -2a + a^2 + 6 - 3a\n\nThe solution is:\n\nf(2-a) = 10 - 7a + a^2
176323
Use the equation y = ax^2 + bx + c\nYou'll will have one equation for each point.\nFor (0,-2), plug in x = 0, and y = -2.\nYou get\n-2 = a(0)^2 + b(0) + c and so you get\n-2 = c\n\nNow the equation becomes\ny = ax^2 + bx - 2\n\nFor the point (2,-2), plug in x = 2 and y = -2\n-2 = a(2)^2 + b(2) -2 or\n-2 = 4a + 2b - 2 Simplify by adding 2 to both sides\n0 = 4a + 2b\n\nFor (3,4), plug in x = 3, and y = 4\n4 = a(3)^2 + b(3) - 2 or \n4 = 9a + 3b - 2  Simplify by adding 2 to both sides\n6 = 9a + 3b\n\nNow these two equations need to be solved simultaneously.\nSolve the first equation for b and then plug that into the second equation and solve for a.\n0 = 4a + 2b  Subtract 2b from both sides\n-2b = 4a  Divide both sides by -2\nb = -2a\nNow replace b with -2a in the equation 6 = 9a + 3b.\n6 = 9a + 3(-2a)\n6 = 9a - 6a\n6 = 3a\n2 = a\nNow plug in 2 for a in the equation b = -2a\nb = -2(2)\nb = -4\n\nNow plug a, b, and c back into the original equation.\ny = ax^2 + bx + c, where a = 2, b = -4, and c = -2\n\ny = 2x^2 - 4x - 2\n\nYou can check your answer by plugging in each of the three points separately to see if you get a true statement each time.