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-2
3x2 + 12x = - 1 ie 3x2 + 12x + 1 = 0 has no rational roots. The irrational roots are [-12 +/- sqrt(132)]/6 = -3.915 and -0.085
1 and 3
y = 3x2+2x-1 Line of symmetry: x = -1/3 Vertex coordinate: (-1/3, -4/3)
Given, 3x2 - 4x = -2 Then, 9x2 - 12x = -6; 9x2 - 12x + 4 = -2 {completing the square} ; 3x - 2 = ±i√2 {sq rt of both sides} ; and 3x = 2 ± i√2. Therefore, x = ⅓(2 ± i√2).
-2
3x2 + 12x = - 1 ie 3x2 + 12x + 1 = 0 has no rational roots. The irrational roots are [-12 +/- sqrt(132)]/6 = -3.915 and -0.085
It is x = +/- 2 depending on whether the second term in the equation is -12x or +12x.
1 and 3
an upside down parabola
y = 3x2+2x-1 Line of symmetry: x = -1/3 Vertex coordinate: (-1/3, -4/3)
The equation is equivalent to: -3x2 - 12x - 1 = 0 [you could change signs to get 3x2 + 12x + 1 = 0 but that is not required] The discriminant is (-12)2 - 4*(-3)(-1) = 144 - 12 = 132
GCF = 12x.24x = 2(12x)36x3 = 3x2(12x)
Given, 3x2 - 4x = -2 Then, 9x2 - 12x = -6; 9x2 - 12x + 4 = -2 {completing the square} ; 3x - 2 = ±i√2 {sq rt of both sides} ; and 3x = 2 ± i√2. Therefore, x = ⅓(2 ± i√2).
-3x2+12x-1 = y Solve the quadratic equation when y = 0 by means of the quadratic equation formula which gives x values of 3.914854216 and 0.085145784. Add these values together and divide them by 2 which is 4/2 = 2 and this is the line symmetry of the parabola. Substitute 2 for x into the original equation to find the value of y: So the vertex is at (2, 11) Remember that the parabola has a maximum value because the coefficient of x2 is negative in other words it will face downwards.
3x2 -12x+24=-10x-20-3x2+6
y = 3x^(2) + 24x - 1 Differentiate and equate to '0' dy/dx = 6x - 24 = 0 6x - 24 = 0 6x = 24 x = 4 is the line of symmetry.