How do you graph the function:
y = 6x(squared) - 12x + 1
Then, how would you find the Axis of Symmetry and the Vertex?
Any help is greatly appreciated
To graph the function y = 6x² - 12x + 1, you can follow these steps:
1. Plot some points:
- Choose a few values for x (e.g., -2, -1, 0, 1, 2) and calculate the corresponding y values.
- For example, when x = -2: y = 6(-2)² - 12(-2) + 1 = 25.
- Plot the points (-2, 25), (-1, 19), (0, 1), (1, -5), and (2, 13).
2. Draw a smooth curve passing through the plotted points.
To find the Axis of Symmetry and the Vertex of a quadratic function, you can use the following formula:
Axis of Symmetry (x-coordinate):
- The formula for the axis of symmetry is given as x = -b / (2a).
- In this case, a = 6 and b = -12.
- Substituting these values into the formula: x = -(-12) / (2 * 6) = 1.
- So, the Axis of Symmetry is x = 1.
Vertex (x-coordinate, y-coordinate):
- To find the y-coordinate of the vertex, substitute the x-coordinate of the axis of symmetry into the original function.
- For x = 1: y = 6(1)² - 12(1) + 1 = -5.
- So, the Vertex is (1,-5).
Now, plot the Axis of Symmetry (x = 1) as a vertical line on the graph, and mark the vertex (1, -5) as a point on the curve.