Question

What is the standard form of the parabola whose equation is 3x² + 24x - 2y + 52 = 0?

Answer 1

The standard form of the parabola equation 3x² + 24x - 2y + 52 = 0 is y = (3/2)x² + 12x - 26.

Step-by-step explanation:

The standard form of the parabola equation 3x² + 24x - 2y + 52 = 0 can be found by rearranging the equation to be in the form y = ax² + bx + c. To do this, we need to isolate the y term.

1. Move all the terms to one side of the equation: 3x² + 24x - 2y + 52 = 0 -> 3x² + 24x - 52 = 2y
2. Divide the entire equation by 2 to isolate y: (3/2)x² + 12x - 26 = y

So, the equation of the parabola in standard form is y = (3/2)x² + 12x - 26.