pete and nick are pilots for the us navy they are being trained to fly plane which are launched from an aircraft carrier their instructor showed them the following graph which represents the flight path pete and nick should take once their plane leaves the deck of the ship it is a graph of the function a(t)=t^2-6t+24
where t represents the amount of time in the air in seconds and a(t) represents the plane's altitude in feet (0 feet represents sea level). the deck of the carrier is 24 feet above sea level after leaving the deck at what altitude will the plane be closet to sea level
To find the altitude at which the plane is closest to sea level, we need to find the minimum point of the graph. This occurs at the vertex of the parabolic function a(t) = t^2 - 6t + 24.
The x-coordinate of the vertex of a parabolic function in the form ax^2 + bx + c is given by the formula x = -b/2a. In this case, a = 1 and b = -6, so the x-coordinate of the vertex is t = -(-6)/(2*1) = 3.
To find the y-coordinate of the vertex, we substitute t = 3 into the function a(t):
a(3) = 3^2 - 6(3) + 24 = 9 - 18 + 24 = 15 feet
Therefore, the plane will be closest to sea level at an altitude of 15 feet.