Graphing the Solution of y = x² – 2x
To graph the equation y = x² – 2x, you can follow these steps:
1. Understand the Equation
This equation is a quadratic equation in the standard form of y = ax² + bx + c, where:
- a = 1 (the coefficient of x²)
- b = -2 (the coefficient of x)
- c = 0 (the constant term)
This tells us that the parabola opens upwards since a > 0.
2. Find the Vertex
The vertex of a parabola given by y = ax² + bx + c can be found using the formula:
x = -b / (2a)
For our equation:
x = -(-2) / (2 * 1) = 2 / 2 = 1
Now substitute x = 1 back into the original equation to find y:
y = (1)² – 2(1) = 1 – 2 = -1
Thus, the vertex is at point (1, -1).
3. Determine the x-Intercepts
To find the x-intercepts, set y = 0:
0 = x² – 2x
Factoring gives:
0 = x(x – 2)
This means:
x = 0 or x = 2
So, the x-intercepts are at points (0, 0) and (2, 0).
4. Determine the y-Intercept
To find the y-intercept, set x = 0:
y = (0)² – 2(0) = 0
The y-intercept is at the point (0, 0) as already found.
5. Plot the Points
Now you can plot the three points we found:
- Vertex: (1, -1)
- x-Intercepts: (0, 0) and (2, 0)
- y-Intercept: (0, 0)
6. Sketch the Parabola
Draw a smooth curve through the points, ensuring it opens upwards. The shape will be symmetric about the vertical line that passes through the vertex.
Final Graph
Once you’ve sketched the parabola, it should resemble the graph below: