how to find the range and domain of y=-18x^2+300x+100

Question

Please explain how to find the range an d domain of the given function.

Answer 1

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.