Question

What is the RANGE of the following graph?
y=-x2- 2x - 5
2

Answer 1

The range would be the number-

Answer 2

See below in bold.

Explanation:

y = -x^2 - 2x - 5

Convert to vertex form:

y = -(x^2 + 2x) - 5

y = - [(x + 1)^2 - 1] - 5

y = -(x + 1)^2 + 1 - 5

y = -(x + 1)^2 - 4

So the vertex of the graph is at (-1 , -4) and it is a maximum because the coefficient of x^2 is negative.

So the range is all values of f(x) up to and including -4.

In interval notation this is (-∞, -4].