The problem describes the path of a soccer ball in the form of a quadratic equation:

$y = -1.6x^2 + 4.48x$

where:

• $x$ is the horizontal distance the ball has traveled,
• $y$ is the vertical height of the ball in meters.

We are asked to determine the height of the ball before it is kicked. This corresponds to the point where $x = 0$ (the ball has not yet traveled horizontally).

Step 1: Substitute $x = 0$ into the equation

$y = -1.6(0)^2 + 4.48(0)$

Simplify: $y = 0$

Final Answer:

The height of the ball before it is kicked is 0 meters. This means the ball started from the ground.

Would you like a detailed explanation about interpreting quadratic equations or any further analysis? Let me know!

Expanding Questions:

1. How do we find the maximum height of the ball using this equation?
2. How can we determine the horizontal distance the ball travels before hitting the ground?
3. What is the significance of the coefficients in the quadratic equation?
4. How do you calculate the vertex of a parabola like this one?
5. Can we model other real-life scenarios with similar equations?

Tip:

When solving a quadratic function, always analyze $x = 0$ for the initial condition—it often represents the starting point.