How to graph:
x(x+3)^2
I understand its a cubic function.
Anyone care to help me with solving and graphing it? thanks.
YOu meant:
graph y = x(x+3)^2
you know you have a root at x=0 and a double root at x = -3 (it touches at (-3,0) )
pick a few more x's and find their matching y's, graph those and you are set.
To graph the equation x(x+3)^2, you can follow these steps:
1. Analyze the equation: The given equation is a cubic function because it contains a higher power of x. The equation also contains a quadratic expression (x+3)^2.
2. Identify key points: To start graphing, find the key points of the cubic function. These include the x-intercepts, y-intercept, and any other important points.
Let's determine these points one by one:
- x-intercepts: Set the equation equal to zero and solve for x to find the x-intercepts (where the graph intersects the x-axis). In this case, let's set x(x+3)^2 = 0. This equation will be satisfied if either x = 0 or (x+3)^2 = 0. Solving (x+3)^2 = 0, we find that x = -3 is the x-intercept.
- y-intercept: To find the y-intercept (where the graph intersects the y-axis), substitute x = 0 into the equation. In this case, y = 0(0+3)^2 = 0. Hence, the y-intercept is (0, 0).
- Additional points: You may choose some additional x-values to evaluate the function and find corresponding y-values. This will help you sketch the curve accurately.
3. Plot the points: After finding the key points from the previous step, plot them on a graph.
- The x-intercept (-3, 0) indicates that the graph passes through (-3, 0). Mark this point on your graph.
- The y-intercept (0, 0) shows that the graph passes through (0, 0). Mark this point as well.
- Choose a few more x-values and calculate the corresponding y-values using the equation. Plot these points as well.
4. Draw the curve: Once you have plotted the key points, draw a smooth curve that passes through these points. For a cubic function, the curve will generally increase or decrease and have both positive and negative slopes.
5. Check and refine: Always double-check your work and ensure that you have accurately plotted the curve. Make any necessary adjustments to ensure that the shape of the graph is consistent with the nature of a cubic function.
Remember, graphing can be subjective to some extent, so your graph may slightly differ in shape or scale from others but should still convey the overall behavior of the equation.