Find the zeros of the function. Then graph the function.
y=(x+3)(x-5)(x-6)
The zero(s) of the function are_____
The zeros of the function are the values of x for which y=0.
To find the zeros, we set y equal to zero and solve for x:
0=(x+3)(x-5)(x-6)
This equation is satisfied when any of the factors (x+3), (x-5), or (x-6) equals zero.
Setting (x+3) equal to zero, we get:
x+3=0
x=-3
Setting (x-5) equal to zero, we get:
x-5=0
x=5
Setting (x-6) equal to zero, we get:
x-6=0
x=6
Therefore, the zeros of the function are x=-3, x=5, and x=6.
To graph the function, we plot the points (-3,0), (5,0), and (6,0) on a coordinate plane and then sketch a curve that passes through these three points. The graph will be a cubic function with x-intercepts at -3, 5, and 6.
To find the zeros of the function, set y equal to zero and solve for x:
0 = (x+3)(x-5)(x-6)
Since the product of three factors is zero, at least one of the factors must be zero:
x+3 = 0 or x-5 = 0 or x-6 = 0
Solving each equation separately:
For x+3 = 0:
x = -3
For x-5 = 0:
x = 5
For x-6 = 0:
x = 6
Therefore, the zeros of the function are -3, 5, and 6.
To graph the function, we can plot the points corresponding to the zeros (-3, 0), (5, 0), and (6, 0). Additionally, we can observe the behavior of the function as it approaches positive and negative infinity.
The graph of the given function would look like:
[Graph]