Adam kicks the football in his backyard. The path of the football when kicked can be represented by the quadratic function y = - 16{x^2} + 85x where x is the horizontal distance (in feet) and y is the height (in feet). How far does Adam kick the football? Express your answer as a decimal rounded to the nearest hundredth.
just factor y to get
y = x(85-16x)
So, what is x when y=0 (that is, when it hits the ground)?
I don't really know you see i know math but word problems are kinda hard for me
To find how far Adam kicks the football, we need to determine the horizontal distance (x) at which the height (y) of the football becomes zero. In other words, we need to find the x-coordinate of the vertex of the quadratic function y = - 16x^2 + 85x, because at the vertex, the height will be at its maximum point before it starts to decrease.
The x-coordinate of the vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula x = -b / (2a). In our case, a = -16 (coefficient of x^2 term) and b = 85 (coefficient of x term).
x = -b / (2a)
x = (-85) / (2(-16))
x = (-85) / (-32)
x ≈ 2.65625
Therefore, Adam kicks the football at a horizontal distance of approximately 2.66 feet, rounded to the nearest hundredth.