How to graph the y= 2x²
Answer (2)
Answer:Here's how to graph the equation y = 2x² and the steps involved: 1. Understanding the Equation - Parabola: The equation y = 2x² represents a parabola. Parabolas are symmetrical curves with a specific shape.- Coefficient: The coefficient '2' in front of the x² term affects the 'steepness' of the parabola. A larger coefficient makes the parabola narrower. 2. Creating a Table of Values To graph the parabola, we'll create a table of x and y values. Choose a range of x-values (both positive and negative) and calculate the corresponding y-values using the equation: x y = 2x² -2 2(-2)² = 8 -1 2(-1)² = 2 0 2(0)² = 0 1 2(1)² = 2 2 2(2)² = 8 3. Plotting the Points Plot the points from the table on a coordinate plane: - (-2, 8)- (-1, 2)- (0, 0)- (1, 2)- (2, 8) 4. Drawing the Parabola Connect the points with a smooth curve to form the parabola. Remember that parabolas are symmetrical, so the curve should mirror itself across the y-axis. Key Points: - Vertex: The lowest point of the parabola is called the vertex. In this case, the vertex is at (0, 0).- Symmetry: The parabola is symmetrical about the y-axis.- Shape: The parabola opens upwards because the coefficient of x² is positive.
Answer:To graph y = 2x², you can follow these steps: 1. Create a table of values: Choose several values for 'x', and calculate the corresponding 'y' values using the equation y = 2x². It's helpful to include both positive and negative values for x, and zero. x y = 2x² -2 8 -1 2 0 0 1 2 2 8 2. Plot the points: On a coordinate plane (with an x-axis and a y-axis), plot each (x, y) pair from your table. 3. Draw the curve: The graph of y = 2x² is a parabola. It's a U-shaped curve. Connect the points you plotted with a smooth, continuous curve. The parabola should be symmetrical about the y-axis (meaning it's a mirror image on either side of the y-axis). The vertex (lowest point) of the parabola will be at (0, 0). Since the coefficient of x² (which is 2) is positive, the parabola opens upwards. Key characteristics of the graph: - Parabola: The graph is a parabola, a U-shaped curve.- Vertex: The vertex (minimum point) is at (0, 0).- Axis of symmetry: The y-axis (x = 0) is the axis of symmetry.- Opens upwards: Because the coefficient of x² is positive (2), the parabola opens upwards.- Steeper than y = x²: The '2' in front of x² makes the parabola narrower (steeper) than the basic parabola y = x². If you have graphing software or a graphing calculator, you can input the equation y = 2x² directly, and it will generate the graph for you automatically.
