Find the zeros of the function. Then graph the function.
y=(x+2)(x-5)(x-6)
The zero(s) of the function are_____
The zeros of the function can be found by setting y = 0:
0 = (x+2)(x-5)(x-6)
This means that either x+2 = 0, x-5 = 0, or x-6 = 0.
Solving these equations, we find:
x+2 = 0: x = -2
x-5 = 0: x = 5
x-6 = 0: x = 6
Therefore, the zeros of the function are x = -2, x = 5, and x = 6.
To graph the function, we can use these zeros and other points to show the shape of the curve. Since the degree of the function is 3, we expect a cubic curve.
Here is the graph of the function:
To find the zeros of the function, we have to solve the equation y = 0.
Given function:
y = (x + 2)(x - 5)(x - 6)
Setting y = 0, we get:
0 = (x + 2)(x - 5)(x - 6)
Setting each factor equal to zero, we have three equations:
1) x + 2 = 0
2) x - 5 = 0
3) x - 6 = 0
Solving each equation:
1) x + 2 = 0
By subtracting 2 from both sides of the equation, we get:
x = -2
2) x - 5 = 0
By adding 5 to both sides of the equation, we get:
x = 5
3) x - 6 = 0
By adding 6 to both sides of the equation, we get:
x = 6
Therefore, the zeros of the function are x = -2, x = 5, and x = 6.
To graph the function, we plot these zeros on the x-axis. The graph will have an x-intercept at each zero of the function. However, without additional information, such as the y-intercept or any other points on the graph, we cannot determine the exact shape or position of the graph.