Respuesta :
The equation which can be represents a parabola in the standard form is given in the option C which is,
[tex]-3x +4y^2 - 2y+ 6 = 0[/tex]
What is equations of the parabolas?
The equation of parabola is the way to represent a parabola in a algebraic expression from using its vertex points.
The general form of the of the parabola can be given as,
[tex]y=a(x-h)^2+k[/tex]
Here, (h, k) are the vertex.
The equation of the parabola in the quadratic equation form can be given as,
[tex]y=ax^2+bx+c[/tex]
Lets check all the option. Equation given in the first option is,
[tex]4x^2 - 2x+ 3y^2 - y +1 = 0[/tex]
This option can not be converted in the above from of parabola.
Equation given in the second option is,
[tex]x^2+ x - 2y^2 - 4y +2 = 0[/tex]
This option can not be converted in the above from of parabola.
Third option is given as,
[tex]-3x +4y^2 - 2y+ 6 = 0\\-3x=-4y^2+2y-6[/tex]
Change the sign of both side of the equation as,
[tex]3x=4y^2-2y+6[/tex]
Divide by number 3 as,
[tex]x=\dfrac{4}{3}y^2-\dfrac{2}{3}y+2[/tex]
This can be compared with the form of parabola equation.
Hence, the equation which can be represents a parabola in the standard form is given in the option C which is,
[tex]-3x +4y^2 - 2y+ 6 = 0[/tex]
Learn more about the equation of parabola here;
https://brainly.com/question/4148030
