To find the maximum height of Laura's soccer ball kick, we'll need to first rewrite the given equation correctly. The description mentions that the model is \( y = -0.004x + 0.489x \). Combining the like terms in the equation gives us:
\[ y = (0.489 - 0.004)x = 0.485x \]
Now, this equation appears to describe a linear function, specifically in the form of \( y = mx + b \). However, we are looking for the maximum height of a projectile, which typically follows a quadratic equation. Thus, we should have an equation in the form of:
\[ y = ax^2 + bx + c \]
Given that the model is linear, we can conclude that something may not be right with the initial data or model; however, if we assume that the correct equation could be quadratic in nature and involves negative acceleration (which is standard for a projectile path), we should find some critical point at which the maximum height occurs.
Let's assume the model is indeed some form of a quadratic equation, say, \( y = ax^2 + bx + c \) where \( a < 0 \) for a downward-opening parabola.
To find the maximum height of a correctly formulated quadratic equation, we would use the vertex formula \( x = -\frac{b}{2a} \), where \( a \) and \( b \) are the coefficients of the respective terms.
Since we have no coefficient for \( x^2 \) in the described model and the form doesn't appear complete, if we suppose there was a projective model, we could infer that Laura could kick a ball much higher than the value indicated by the previously written linear form.
However, based on the information provided, it is impossible to accurately calculate the maximum height without the correct quadratic form. If you could verify the full equation of motion or any related values for standard projectile motion being analyzed, please provide that for more precise calculation.
For now, with only the provided form, it doesn't accurately represent projectile motion, and so we cannot provide a reasonable estimated maximum height.
If you meant an assumed quadratic equation or specific heights, please provide further clarity for accurate calculations.