How do you graph the function y=-1/3x^2-4x+1 and identify the domain and range?

1 Answer
Jun 11, 2017

Domain: (-oo, +oo)
Range: (-oo, 13]

Explanation:

y = -1/3x^2-4x+1

y is defined forall x in RR
Hence the domain of y is (-oo, +oo)

Consider the standard form of the quadratic: ax^2+bx+c
It is known that the critical point will be where x=(-b)/(2a)

In this case, since the coefficient of x^2 <0, the critical value will be a maximum.

:. for y_"max" x= 4/(-(2/3))

= -6

y_"max" = y(-6) = -12+24+1 = 13

Hence the range of y is (-oo, 13]

This can be seen from the graph of y below.

graph{(-x^2)/3-4x+1 [-41.1, 41.1, -20.6, 20.5]}