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
My answer is b.
is it b
To find the axis of symmetry for the function h(t) = -16t^2 + 48t, we can use the formula t = -b/2a, where a, b, and c are the coefficients of the quadratic equation in standard form.
In this case, the coefficient of t^2 is -16, and the coefficient of t is 48. Plugging these values into the formula, we get:
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, it takes 1.5 seconds for the ball to reach the highest point in its trajectory.
To find the axis of symmetry for the function h(t) = -16t^2 + 48t, we can use the formula:
Axis of Symmetry = -b / (2a),
where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c.
In this case, a = -16 and b = 48.
Plugging these values into the formula, we have:
Axis of Symmetry = -48 / (2 * (-16))
= -48 / (-32)
= 1.5
Therefore, the correct answer is t = 1.5. This represents the time in seconds it takes for the ball to reach its maximum height and then fall back to the ground.