John R. answered 05/14/13
John R: Math, Science, and History Teacher
Since there are no variables under radicals or in denominators, the domain is all real numbers.
Since the equation is a quadratic, the maximum or minimum value will be located at the vertex.
To find the x value of the vertex of the parabola, divide the opposite coefficient of the x term by 2 times the coefficient of the x2 term.
x = -300/[2*(-18)]
x = 25/3
Substituting the x value of the vertex into the equation, we can find the y value of the vertex.
y = -18(25/3)2 + 300(25/3) + 100
y = -1250 + 2500 + 100
y = 1350
Since the coefficient in front of the x2 term is negative, the vertex is the maximum (highest point of the function). The equation goes down forever on each side.
The range is y ≤ 1350.