Suppose Paul kicks a soccer ball straight up into the air with an initial velocity of 96 feet per second. The function f(x) = -16t2 + 96t gives the height, in feet, of the soccer ball after t seconds.Show all work to find the axis of symmetry algebraically. You must show all work for credit.
the t of the vertex is -b/(2a)
= -96/(-32)
= 3
so t = 3 is the axis of symmetry
btw, your function should have said
f(t) = -16t^2 + 96t, there was no x in sight.
To find the axis of symmetry algebraically, we need to determine the value of t that represents the vertex of the quadratic equation. The axis of symmetry is the vertical line that passes through the vertex and divides the parabola into two symmetric parts.
The equation given, f(x) = -16t^2 + 96t, represents a quadratic function in the form of f(t) = at^2 + bt + c. In this case, a = -16, b = 96, and c = 0 (since there is no constant term).
The t-coordinate of the vertex can be found using the formula t = -b / 2a. Plugging the values of a and b into the formula:
t = -96 / (2 * -16)
t = -96 / (-32)
t = 96 / 32
t = 3
Therefore, the axis of symmetry of the quadratic equation is represented by t = 3.