graph y=x2,y=2x2 and y=1/2x2 on the same
To graph the equations y = x^2, y = 2x^2, and y = (1/2)x^2 on the same graph, we will follow these steps:
Step 1: Determine the domain and range
Step 2: Find a few points for each equation
Step 3: Plot the points on a graph
Step 4: Draw the curves connecting the points for each equation
Let's go through each step in detail:
Step 1: Determine the domain and range
Since all the equations are quadratic functions, their domains are all real numbers. For the range, we can see that the minimum value of y is 0 for all equations. Therefore, the range for each equation is y ≥ 0.
Step 2: Find a few points for each equation
To graph each equation, we need to find a few points. Here are some points for each equation:
For y = x^2:
- x = -2, y = 4
- x = -1, y = 1
- x = 0, y = 0
- x = 1, y = 1
- x = 2, y = 4
For y = 2x^2:
- x = -2, y = 8
- x = -1, y = 2
- x = 0, y = 0
- x = 1, y = 2
- x = 2, y = 8
For y = (1/2)x^2:
- x = -2, y = 2
- x = -1, y = 1/2
- x = 0, y = 0
- x = 1, y = 1/2
- x = 2, y = 2
Step 3: Plot the points on a graph
Now, let's plot these points on a graph. Choose a scale that allows all the points to fit comfortably.
Step 4: Draw the curves connecting the points for each equation
Now, connect the points for each equation, creating a curve. The curve for y = x^2 will be a U-shaped curve opening upwards. The curve for y = 2x^2 will also be a U-shaped curve, but steeper. Finally, the curve for y = (1/2)x^2 will be less steep than y = x^2.
After following these steps, you will have a graph with all three quadratic equations (y = x^2, y = 2x^2, and y = (1/2)x^2) plotted on it.
To graph the equations y = x^2, y = 2x^2, and y = (1/2)x^2 on the same graph, you can follow these steps:
Step 1: Choose a range for the x-values: Determine the range of numbers for the x-values that you want to plot on the graph. For example, let's choose a range from -5 to 5.
Step 2: Generate the corresponding y-values: Plug in the chosen x-values into each equation to calculate the corresponding y-values. For example, for the equation y = x^2, when x = -5, y = (-5)^2 = 25. Similarly, for the equation y = 2x^2, when x = -5, y = 2(-5)^2 = 50. Repeat this process for all x-values within the chosen range.
Step 3: Plot the points: Using the calculated x and y-values, plot the points for each equation on the graph. For example, for the equation y = x^2, plot the points (-5, 25), (-4, 16), (-3, 9), (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4), (3, 9), (4, 16), (5, 25). Repeat this process for the other two equations.
Step 4: Draw the curves: Once all the points are plotted, connect them smoothly to form curved lines that represent each equation. Keep in mind that the graph for y = x^2 should look like a U-shaped curve, while the graph for y = 2x^2 should be a steeper U-shaped curve, and the graph for y = (1/2)x^2 should be a wider U-shaped curve.
Step 5: Label the axes and add a legend (optional): Add labels to the x and y axes to indicate what variables they represent. You can also add a legend to the graph to identify which curve represents which equation.
By following these steps, you should be able to graph the equations y = x^2, y = 2x^2, and y = (1/2)x^2 on the same graph.