How many x-intercepts does the graph of y = -(x + 1)2 - 2 have?
Solution:
Given, y = -(x + 1)2 - 2
We have to find the x-intercepts of the function.
The X-intercept is the point where the point crosses the x-axis
Here, y = 0
Put y = 0
-(x + 1)2 - 2 = 0
-(x + 1)2 = 2
Now, (x + 1)2 = -2
Taking square root,
(x + 1) = √-2
The square of any real number cannot be negative.
Look at the graph of this function.
From the graph, it is clear that the graph does not cross the x-axis.
Therefore, the given function has no x-intercepts.
How many x-intercepts does the graph of y = -(x + 1)2 - 2 have?
Summary:
The graph of y = -(x + 1)2 - 2 does not have x-intercepts.