What are the steps to graph a quadratic equation?
To graph a quadratic equation, follow these steps:
1. Understand the quadratic equation:
- A quadratic equation is of the form: y = ax^2 + bx + c, where a, b, and c are constants.
- The equation represents a curve called a parabola.
2. Find the vertex:
- The vertex is the highest or lowest point on the parabola.
- The x-coordinate of the vertex is given by: x = -b / (2a).
- Substitute the value of x in the equation to find the y-coordinate of the vertex.
3. Find the y-intercept:
- The y-intercept occurs when x = 0.
- Substitute x = 0 in the equation to find the y-intercept.
4. Find the x-intercepts (or roots):
- The x-intercepts are the points where the parabola crosses the x-axis.
- Set y = 0 in the equation and solve for x using factorization, completing the square, or the quadratic formula.
5. Determine the axis of symmetry:
- The axis of symmetry is a vertical line that passes through the vertex.
- The equation for the axis of symmetry is x = -b / (2a).
6. Plot the points:
- Plot the vertex, y-intercept, and x-intercepts on the coordinate plane.
7. Choose additional points:
- Choose some other x-values, both to the left and right of the vertex.
- Substitute these x-values into the equation to find the corresponding y-values.
8. Draw the graph:
- Connect the plotted points using a smooth curve.
- Extend the graph beyond the plotted points if needed.
Remember, graphing software and calculators can also help visualize the graph by automating some of these steps.