Why are these poor models for a parabola, Where a ball starts a a certain point and then is hit to reach a maximum height (vertex) and then lands at a certain point

i. y = -0.002x(x - 437.1)
ii. y = -0.5x + 216x + 3
iii. y = -0.002x + 0.879x + 3.981
iv. y = -0.002x + 0.8732x - 3.981

Thanks!

To determine whether these equations are poor models for a parabola representing the motion of a ball being hit, we need to check if they satisfy the characteristics of a parabola. Specifically, we want to ensure that the equation represents a parabolic path with a maximum height and landing at a certain point.

A general equation for a parabola is y = ax^2 + bx + c, where a, b, and c are constants. The x-axis represents time, and the y-axis represents the height of the ball.

i. y = -0.002x(x - 437.1)
This equation is a quadratic equation since it is in the form of y = ax^2 + bx. It includes a vertex-form representation (x - h)^2, where h is the x-coordinate of the vertex. In this case, the vertex form is (x - 437.1), suggesting that the vertex occurs at x = 437.1. However, the coefficient of x^2 (-0.002) is negative, meaning the parabola opens downward instead of upward. This indicates that the ball is not reaching a maximum height but is instead descending in height.

ii. y = -0.5x + 216x + 3
This equation is not a quadratic equation since it lacks an x^2 term. Instead, it represents a linear equation due to the presence of an x term. Linear equations represent a straight line rather than a parabolic path, so this equation is not suitable for modeling a ball's parabolic motion.

iii. y = -0.002x + 0.879x + 3.981
This equation is also not a quadratic equation since it lacks an x^2 term. Similar to the previous equation, it represents a linear equation rather than a parabolic path, making it an inappropriate model for the ball's motion.

iv. y = -0.002x + 0.8732x - 3.981
Like the previous equations, this equation is also not a quadratic equation due to the absence of an x^2 term. Consequently, it represents a linear equation and is not suitable for modeling parabolic motion.

In conclusion, none of the given equations (i, ii, iii, iv) are appropriate models for a parabola representing the motion of a ball starting at a certain point, reaching a maximum height, and landing at a specific point. A valid parabolic equation for this motion would require an x^2 term to represent the characteristic shape of a parabola.