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What is the x-coordinate of the vertex of the parabola whose equation is y 3x2 9x?
Without an equality sign it can not be considered to be an equation and the - or + value of 9x has not been given
What is the shape of the curve y equals 3x squared plus x minus 2?
A parabola You can find the peak of this parabola by taking it's derivative and finding the point where it's slope is equal to zero: y = 3x2 + x - 2 y' = 6x + 1 Let y' = 0 0 = 6x + 1 x = -1/6 Now find the y co-ordinate: y = 3(-1/6)2 + (-1/6) - 2 y = 3/18 - 1/6 - 2 y = -2 So this parabola's vertex will be located at the point (-1/6, -2).
How do you work out the solutions for 3x-2y equals 1 and 3x square-2y square plus 5 equals 0?
How to solve: 3x - 2y = 1 3x2 - 2y2 + 5 = 0 Rearrange the first equation to make x or y the subject (that is x = something or y = something) and then substitute into the second equation and solve that: 3x - 2y = 1 => y = (3x - 1)/2 3x2 - 2y2 + 5 = 0 => 3x2 - 2((3x - 1)/2)2 + 5 = 0 [substitute for y] => 3x2 - 2(9x2 - 6x + 1)/4 + 5 = 0 [expand the square term] => 3x2 - (9x2 - 6x + 1)/2 + 5 = 0 [spot that 2w/4 is the same as w/2] => 6x2 - (9x2 - 6x + 1) + 10 = 0 [multiply equation by 2] => 6x2 - 9x2 + 6x - 1 + 10 = 0 [remove the brackets by multiplying by -1 as it is -1 x (..)] => -3x2 + 6x + 9 = 0 [collect together terms] => 3x2 - 6x - 9 = 0 [multiply whole equation by -1] => x2 - 2x - 3 = 0 [divide whole equation by 3] => (x - 3)(x + 1) =0 [factorize) => x = 3 or -1 [as one factor or the other must be zero] Now use first equation to find corresponding y terms: x = 3:y = (3 x (3) - 1) / 2 = 8 / 2 = 4 x = -1: y= (3 x (-1) - 1) /2 = -4 / 2 = -2 So the solution is the (x, y) pairs, or points, (3, 4) and (-1, -2). The answer can be checked using the second equation: (3, 4): 3(3)2 - 2(4)2 + 5 = 3 x 9 - 2 x 16 + 5 = 27 - 32 + 5 = 0 (-1, -2): 3(-1)2 - 2(-2)2 + 5 = 3 x 1 - 2 x 4 + 5 = 3 - 8 + 5 = 0
How many vertices in a 3D triangle?
6 because 3x2
What is the quadratic trinomial 27x2-90x 27?
If you mean: 27x2-90x+27 then divide all terms by 9 which is then 3x2-10x+3 And when factored it is: (3x-1)(x-3)
