Final answer:
The question is identifying the correct equation of a parabola, which represents the trajectory of a projectile and is expressed in a quadratic form. The quadratic formula is applied to solve such equations.
Step-by-step explanation:
The student is asking for the equation of a parabola, which is a quadratic equation of the form y = ax + bx². This form is typical of the trajectory of a projectile. To derive the equation of a parabola from the trajectory of a projectile, one would use the horizontal displacement x = Voxt to solve for time t and then substitute into the expression for vertical displacement y = Voyt - (1/2)gt², resulting in a quadratic equation where a and b are constants.
When solving a quadratic equation of the form ax² + bx + c = 0, the quadratic formula x = (-b ± √(b² - 4ac))/(2a) is used to find the solutions for x.