Carla is watching a professional baseball game on television and sees a batter hit a home run over the fence. A graphic overlay comes up during the replay that shows how high and far the ball traveled in feet. Carla recognizes the shape to be a quadratic and wants to write an equation to represent the function. Which of the following functions accurately models the graph?

Question

(1 point)

The height reached by the ball, h (x), is given by the equation h(x) = 43 1920 (2-90)2 + 215, where x represents the horizontal distance.

The height reached by the ball, h(x), is given by the equation h( x)= 43/(1, 620) * (x - 90) ^ 2 + 215 , where x represents the horizontal distance.

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The height reached by the is given by the equation h (x) = - 18/(9, 245) * (x - 215) ^ 2 + 90, wh x represents the horizontal distance.

The height reached by the ball, u(x), i given by the equation h (x) where x represents the horizontal distance. = 18/(9, 245) * (x - 215) ^ 2 + 90 ,

Answer 1

To determine which equation accurately models the height of the baseball in terms of its horizontal distance, we can analyze each option. In general, the shape of a baseball's trajectory is a downward-opening parabola, which suggests the height function should have a negative leading coefficient.

Let’s examine the options:

1. h(x) = 43 1920 (2-90)² + 215
   This equation seems to have a formatting issue and isn’t clearly defined. It does not show a traditional quadratic structure because it’s not clear what "43 1920" means.

2. h(x) = 43/(1, 620) * (x - 90)² + 215
   This function has a positive leading coefficient, suggesting that it opens upwards, which is not characteristic of a projectile’s height function. Thus, it cannot represent the height of a ball in flight.

3. h(x) = -18/(9, 245) * (x - 215)² + 90
   This equation has a negative coefficient, which suggests that it opens downwards (correct for a projectile). This looks like a reasonable choice, but we need clarification on the specific value (the numbers in the denominator "9, 245") and what they represent in context.

4. h(x) = 18/(9, 245) * (x - 215)² + 90
   Similar to option 2, this has a positive leading coefficient. Therefore, it cannot correctly represent the parabola's shape for a home run ball.

Given these assessments, the most reasonable function that models the height of the ball is:

h(x) = -18/(9, 245) * (x - 215)² + 90

This function represents a downward-opening parabola, conforming to what is expected from a trajectory of a baseball hit as a home run.

Please verify the coefficients and constants based on the specific context of the game to ensure accuracy in modeling.