1. **Problem Statement:** Teresa kicks a ball towards a goal post 5 meters away that is 1 meter high. We need to determine mathematically whether the ball went into the goal post. 2. **Assumptions and Known Variables:** - Distance to goal post, $d = 5$ meters - Height of goal post, $h = 1$ meter - We need the height of the ball at $x = 5$ m to compare with $h$ 3. **Mathematical Model:** Assuming the ball follows a projectile motion path, the height $y$ as a function of horizontal distance $x$ can be modeled by a quadratic equation: $$y = ax^2 + bx + c$$ where $a, b, c$ depend on initial speed, angle, and initial height. 4. **Data Needed:** Without explicit initial velocity, angle, or height function, we cannot determine $y$ at $x=5$. 5. **If we had the equation, to justify mathematically, we check:** $$y(5) \geq 1$$ if true, ball is at or above the goal post height. **Conclusion:** With given information, it is not possible to conclusively determine if the ball went into the goal post mathematically without further data about ball trajectory or initial conditions.