How many x-intercepts are on the graph of y = −(x + 5)^2 + 2?
To find the x-intercepts, set y = 0 and solve for x:
0 = -(x + 5)^2 + 2
-(x + 5)^2 = -2
(x + 5)^2 = 2
Taking the square root of both sides:
x + 5 = ±√2
Simplifying further:
x = -5 ± √2
This gives us two possible x-intercepts, when x = -5 + √2 and x = -5 - √2. So, there are two x-intercepts on the graph of y = -(x + 5)^2 + 2.