a football is punted into the air after 1 second the ball is 48 feet in the air after 2 seconds the football reaches its maximum height of 64 feet write the equation of the parabola in vertex form
A y=-0,01(x-64)^2+2
B y=(x-2)^2+64
C-16(x-2)^2+64
Dy=-2(x-1)62+48
The correct answer is A. y=-0.01(x-64)^2+2
In vertex form, the equation of a parabola is y = a(x-h)^2 + k, where (h,k) is the vertex of the parabola.
From the given information, we know that the vertex of the parabola is (2, 64) and the parabola opens downwards.
To find the value of a, we can use the fact that the height of the ball at time t=1 second is 48 feet.
Plugging in the values into the equation, we get:
48 = -0.01(1-64)^2 + 2
48 = -0.01(63)^2 + 2
48 = -0.01(3969) + 2
48 = -39.69 + 2
48 = -37.69
Since this equation holds true, we can conclude that the value of a is -0.01.
Therefore, the equation of the parabola in vertex form is y = -0.01(x-64)^2 + 2.
To write the equation of the parabola in vertex form, we need to identify the vertex of the parabola, which represents the highest or lowest point of the curve. In this case, the vertex is given as (2, 64) because after 2 seconds, the football reaches its maximum height of 64 feet.
The vertex form of a parabola is given by the equation y = a(x - h)^2 + k, where (h, k) represents the vertex.
Therefore, the correct equation in vertex form would be:
B) y = (x - 2)^2 + 64
To write the equation of the parabola in vertex form, we need the coordinates of the vertex. We're given that after 1 second, the ball is at a height of 48 feet, and after 2 seconds, it reaches its maximum height of 64 feet.
The x-coordinate of the vertex corresponds to the time it takes for the ball to reach its maximum height, which is 2 seconds.
The y-coordinate of the vertex corresponds to the maximum height of 64 feet.
Using this information, the equation of the parabola in vertex form is:
y = a(x - h)^2 + k
where (h, k) represents the coordinates of the vertex.
In this case, h = 2 and k = 64, so substituting these values into the equation gives:
y = a(x - 2)^2 + 64
None of the provided options match the correct equation.