HELP ASAP 25 POINTS

(1).

(2). 1 minute

Step-by-step explanation:

They want you to factorize the equation in such a way that the vertex appears as a number in the equation; and you do that by using a method called completing the squareHere is our equation: We factor it by completing the square: But first remember this:A quadratic equation has the general form Where a and b are the numbers before x squared and x respectively, and c is the number without an x, and f(x) is the value dependent on xIn this case x is tSo the steps are as followsEquate the equation to zero: Divide each term by the (a) of the equation in this case is it -4, and we get: Then take the new (c) to the other side of the equation, in the case we add 8 to both sides to get: Now the tricky part, you have to add to both sides of the equation the square of half of the coefficient of t or number before t, not t squared just t and you get: Now the left side is in the square form, or it just means when you factor the left side, you get it as the square of a certain single term, in this case we get: When we simplify we get: Now any equation in this form, will give you the vertex when you equate the term in parenthesis to zero, and simplify: is the value of the t or time at the vertex To write the equation again, multiply every term with the (a) you used to get: , and this is the equation for #(1)Now here is why we needed to get the vertex; the vertex tells us at what point the height either reaches its maximum/highest level, or where it reaches its minimum/lowest level So since the time (t) at the vertex is 1, in order to find the height at this time, just plug it into the equation: So that's the height at the vertexNow it can either be the maximum/highest height or the minimum/lowest height, in order to know this we check as followsRemember the (a) we used to factor the equation? -4, if the (a) value of a quadratic function is less than 0, then it is a maximum equation, mean whatever vertex you get will be the point where the equation reaches its biggest value.So at a height of 36 meters, and a time of 1 minute, the craft reaches its highest point.