Using his driver on the 7th tee, Chris hits an excellent shot, right down the middle of the fairway. The ball follows the parabolic path shown in the figure, described by the quadratic function: h(x)=0.5x-0.002x^2. This relates the height, h, of the ball above the ground to the distance x it has traveled down the course. Distances are measures in feet.
What is the ball’s maximum height above the ground and what distance x, from the tee, does this occur at?
Please teach me this question..
Well, looks like Chris is quite the golfer! To find the ball's maximum height above the ground and the distance from the tee where this occurs, we can use the quadratic function h(x) = 0.5x - 0.002x^2.
The maximum height of the ball corresponds to the vertex of the parabolic function. To determine the x-coordinate of the vertex, we can use the formula x = -b / (2a). In this case, a = -0.002 and b = 0.5.
Substituting the values, we get x = -0.5 / (2 * -0.002) = 0.5 / 0.004 = 125.
So, the ball reaches its maximum height at a distance of 125 feet from the tee.
To find the actual maximum height, we substitute this x-value back into the function h(x). Plugging x = 125 into the function h(x) = 0.5x - 0.002x^2 gives us: h(125) = 0.5 * 125 - 0.002 * 125^2.
Calculating this expression gives h(125) = 62.5 - 0.002 * 15625 = 62.5 - 31.25 = 31.25.
Therefore, the ball's maximum height above the ground is 31.25 feet.
I hope that helps! Keep up the good work, Chris!
To find the maximum height of the ball and the distance from the tee where it occurs, we need to find the vertex of the parabolic function.
The general form of a quadratic function is h(x) = ax^2 + bx + c, where a, b, and c are constants.
In this case, h(x) = 0.5x - 0.002x^2. So, a = -0.002, b = 0.5, and c = 0.
The x-coordinate of the vertex can be found using the formula x = -b / (2a).
Plugging in the values, x = -(0.5) / (2(-0.002)). Simplifying, x = 125.
So, the maximum height occurs at a distance of 125 feet from the tee.
To find the maximum height, substitute this value into the equation h(x) = 0.5x - 0.002x^2.
h(125) = 0.5(125) - 0.002(125)^2.
Simplifying, h(125) = 62.5 - 0.002(15625) = 62.5 - 31.25 = 31.25.
Therefore, the ball's maximum height above the ground is 31.25 feet.
To find the maximum height of the ball above the ground and the distance from the tee at which it occurs, we can use the equation of the quadratic function provided: h(x) = 0.5x - 0.002x^2
The equation is in the form of a quadratic function, which is a parabola. In this case, the parabola opens downward because the coefficient of the x^2 term is negative (-0.002).
To find the maximum height, we need to determine the vertex of the parabola. The x-coordinate of the vertex gives us the distance from the tee at which the ball reaches its maximum height, and the y-coordinate gives us the maximum height itself.
The x-coordinate of the vertex can be found using the formula: x = -b / (2a), where a and b are the coefficients of the x^2 and x terms, respectively.
In the equation h(x) = 0.5x - 0.002x^2, a = -0.002 and b = 0.5.
Substituting these values into the formula, we get: x = -(0.5) / (2 * (-0.002)) = 125.
Therefore, the ball reaches its maximum height at a distance of 125 feet from the tee.
To find the y-coordinate (maximum height), we substitute this x-coordinate into the equation h(x):
h(125) = 0.5 * 125 - 0.002 * (125)^2
= 62.5 - 0.002 * 15625
= 62.5 - 31.25
= 31.25
Hence, the maximum height of the ball above the ground is 31.25 feet.