A soccer ball is kicked toward the goal. The height of the ball is modeled by the function h(t) = −16t2 + 48t where t equals the time in seconds and h(t) represents the height of the ball at time t seconds. What is the axis of symmetry, and what does it represent?
t = 1.5; it takes 1.5 seconds to reach the maximum height and 3 seconds to fall back to the ground.
t = 1.5; it takes 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground.
t = 3; it takes 3 seconds to reach the maximum height and 3 seconds to fall back to the ground.
t = 3; it takes 3 seconds to reach the maximum height and 6 seconds to fall back to the ground.
To find the axis of symmetry of a quadratic function, you can use the formula x = -b/2a, where the quadratic function is in the form ax^2 + bx + c.
In the case of the given function h(t) = -16t^2 + 48t, we can identify that a = -16 and b = 48.
Using the formula x = -b/2a, we can substitute the values of a and b into the formula:
t = -48 / (2 * (-16))
t = -48 / (-32)
t = 1.5
Therefore, the axis of symmetry is t = 1.5.
The axis of symmetry represents the time at which the ball reaches its maximum height. In this case, since the ball reaches its maximum height after 1.5 seconds, the axis of symmetry represents that moment.
In order to find the axis of symmetry, you need to set the equation up for graphing in the form
(x−h)2=y−k