Identify the zeros for the function and sketch a graph.
y equals x left parenthesis x minus 2 right parenthesis left parenthesis x plus 3 right parenthesis
(1 point)
Responses
x equals 0, x equals 2, x equals negative 3
A cubic function is graphed on a coordinate plane. It crosses the x-axis at negative 3, 0, and 2. The end behavior is down and up.
Image with alt text: x equals 0, x equals 2, x equals negative 3 Image with alt text: A cubic function is graphed on a coordinate plane. It crosses the x-axis at negative 3, 0, and 2. The end behavior is down and up.
x equals 0, x equals 2, x equals negative 3
A cubic function is graphed on a coordinate plane. It crosses the x-axis at negative 3, 0, and 2. The end behavior is up and down.
Image with alt text: x equals 0, x equals 2, x equals negative 3 Image with alt text: A cubic function is graphed on a coordinate plane. It crosses the x-axis at negative 3, 0, and 2. The end behavior is up and down.
x equals 0, x equals negative 2, x equals 3
A cubic function is graphed on a coordinate plane. It crosses the x-axis at negative 2, 0, and 3. The end behavior is down and up.
Image with alt text: x equals 0, x equals negative 2, x equals 3 Image with alt text: A cubic function is graphed on a coordinate plane. It crosses the x-axis at negative 2, 0, and 3. The end behavior is down and up.
x equals 0, x equals negative 2, x equals 3
A cubic function is graphed on a coordinate plane. It crosses the x-axis at negative 2, 0, and 3. The end behavior is up and down.
The correct response is: x equals 0, x equals 2, x equals negative 3.
A cubic function is graphed on a coordinate plane. It crosses the x-axis at negative 3, 0, and 2. The end behavior is up and down.
The zeros for the function y = x(x-2)(x+3) are x = 0, x = 2, and x = -3. The sketch of the graph shows that the cubic function crosses the x-axis at x = -3, x = 0, and x = 2. The end behavior of the graph is down and up.
To identify the zeros of the function, you need to find the values of x for which y equals 0. In this case, the function is y = x(x - 2)(x + 3).
To find the zeros, set y equal to 0 and solve for x:
0 = x(x - 2)(x + 3)
To have a product equal to zero, at least one of the factors must be zero. So set each factor equal to zero and solve for x:
x = 0, (x - 2) = 0, (x + 3) = 0
Solving each equation, we get x = 0, x = 2, and x = -3. These are the zeros or x-intercepts of the function.
To sketch the graph, plot the points (0, 0), (2, 0), and (-3, 0) on a coordinate plane. These are the x-intercepts where the function crosses the x-axis.
Since the function is cubic (degree 3), it will have an end behavior that starts down (from the left side) and goes up (to the right side) or vice versa.
With this information, you can sketch a graph of the function with the x-axis and the points (0, 0), (2, 0), and (-3, 0) labeled as the x-intercepts.
Note: The graph can be further refined by plotting additional points and considering the behavior of the function between the x-intercepts, but for the given question, plotting the x-intercepts and understanding the end behavior is sufficient.