Answer:
With this algebraic representation of physics, we can also apply the mathmatical concept of quadratics to derive the components from this function. You can use the line of symmetry: x = -b/2a. To find the minimum or maximum height because of its association with the vertex. This function is in the standard quadratic form: ax^2 + bx + c where x is t. According to this instance, a being -16, b being 24, and c being 8. t = -b/2a → -24/-32 = 3/4 which also represents the maximum value because a is negative so it is opening downward.
To find the max height, substitute the value of x back into the equation f(3/4) = -16(3/4)^2 + 24(3/4) + 8 →
-9 + 18 + 8 = 17ft [maximum height]
We already solved for the time (x) in terms of t which is 3/4 sec [time of maximum height].
