Question

Emily threw a ball up in the air from her tree house. It followed the given by the fparabola y=-2x²+14x+60, where x is the ice from the tree house (in feet ), and y is the height of the ball (in feet ).

At what distance away from the tree house did the ball strike the ground?

Answer 1

To find the distance away from the tree house where the ball strikes the ground, we can use the quadratic formula to solve the equation y = -2x² + 14x + 60. The solutions for x are approximately 3.316 feet and approximately 5.684 feet.

Step-by-step explanation:

To find the distance away from the tree house where the ball strikes the ground, we need to determine the x-coordinate where y = 0. In other words, we need to find the roots of the quadratic equation y = -2x² + 14x + 60.

To solve this equation, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a). Plugging in the values from the equation, we have a = -2, b = 14, and c = 60.

Using the quadratic formula, we get:

x = (-14 ± √(14² - 4(-2)(60))) / (2(-2)).

After simplifying, we get two possible solutions for x, which are x ≈ 3.316 and x ≈ 5.684. Therefore, the ball strikes the ground at a distance of approximately 3.316 feet or approximately 5.684 feet away from the tree house.