To model the height of the soccer ball kicked by Aria in vertex form, we need to consider the quadratic function. In this case, the ball reaches a maximum height before hitting the ground.
Here is how we can set up the equation in vertex form:
1. Identify the vertex form of a quadratic function: \( f(x) = a(x-h)^2 + k \), where (h, k) represents the vertex of the parabola.
2. The vertex form helps us determine the maximum height (vertex) of the ball before it falls back to the ground.
3. Given that the ball reaches a height of 14.1 feet 1.3 seconds after the kick, we can use this information to find the vertex.
4. Since the maximum height occurs at the vertex, the values of x and f(x) at the vertex are crucial in determining the quadratic function that models this scenario.
5. By substituting the values of x and f(x) into the vertex form, we can determine the specific quadratic function that represents the height of the soccer ball as it moves through the air.
By following these steps and plugging in the provided information about the height of the ball at specific times, you can derive the quadratic function that accurately models this context in vertex form.
