Question

You are out on the river in a boat and a fish jumps up out of the water and over your boat, from the left side to the right.For simplicity we will assume the boat is not on either bank (or in the parking lot).The path of the fish can be modeled by one of the equations below, and forms a parabola opening down. Let's consider the surface of the water to be the x-axis, the bank to be the y-axis, and the river is 50 feet wide.

(1) The following function could represent this situation: F(x) = -x + 10x -21 .Explain why the others do not fit the story.
a. F(x) = -x?- 10x - 16
b. F(x) = x2 - 6x + 13
C. F(x) = -x + 6x -13

Answer 1

The correct function for the fish's path over the boat is F(x) = -x² + 10x - 21 since it represents a parabola that opens downward and has the fish entering and leaving the water at the river's edges.

Step-by-step explanation:

The correct function to represent the fish jumping over the boat and forming a parabola opening downward is F(x) = -x² + 10x - 21, where the coefficient of x² is negative, indicating a parabola opening down. The provided function shows that when x = 0 and x = 50 (the width of the river), F(x) will be negative, implying that the fish starts and lands in the water. Options a, b, and c are incorrect because:

• Option a, F(x) = -x² - 10x - 16, represents a downward opening parabola, but it incorrectly suggests that the fish starts below the water level and lands further below the water level on the opposite side since the y-intercept and the value at x=50 would both be negative.
• Option b, F(x) = x² - 6x + 13, represents an upward opening parabola which does not match the question data stating a parabola opening down.
• Option c, F(x) = -x² + 6x - 13, also opens downwards but the coefficients would not place the fish in the correct starting and landing positions as described.