Question
You and your grandfather attend a live NBA game. One of the players is getting ready to make a free throw. The equation y=−0.05x2+0.8x+6
represents the trajectory of the ball from when it leaves the player’s hands. The player is 6 feet tall. At what distance from the player does the ball reach its maximum height
represents the trajectory of the ball from when it leaves the player’s hands. The player is 6 feet tall. At what distance from the player does the ball reach its maximum height
Answers
GPT 3.5
To find the distance from the player at which the ball reaches its maximum height, we need to determine the x-coordinate of the vertex of the parabolic equation representing the trajectory of the ball.
The vertex of a parabola given in the form y = ax^2 + bx + c is located at the x-coordinate x = -b/(2a).
In this case, the equation for the trajectory of the ball is y = -0.05x^2 + 0.8x + 6.
Comparing this with the standard form of a quadratic equation y = ax^2 + bx + c, we have a = -0.05 and b = 0.8.
Therefore, the x-coordinate of the vertex is x = -0.8 / (2 * -0.05) = -0.8 / (-0.1) = 8.
So, the ball reaches its maximum height at a distance of 8 feet from the player.
The vertex of a parabola given in the form y = ax^2 + bx + c is located at the x-coordinate x = -b/(2a).
In this case, the equation for the trajectory of the ball is y = -0.05x^2 + 0.8x + 6.
Comparing this with the standard form of a quadratic equation y = ax^2 + bx + c, we have a = -0.05 and b = 0.8.
Therefore, the x-coordinate of the vertex is x = -0.8 / (2 * -0.05) = -0.8 / (-0.1) = 8.
So, the ball reaches its maximum height at a distance of 8 feet from the player.