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Given the parabola \( y = ax^2 + bx + c\)
| Conclusion | Example: \( y = 2x^2 - 4x - 16\) | |
|---|---|---|
| a > 0 | ||
| a < 0 | ||
| a = 0 | ||
| |a| > 1 | ||
| |a| < 1 | ||
| Axis of Symmetry: | ||
| Nature of x-intercepts determined by Discriminant D: | ||
| D > 0 and is a perfect square | ||
| D > 0 and is not a perfect square | ||
| D = 0 | ||
| D < 0 | ||
| x-intercepts: | ||
| y-intercept: | ||
| Distane from Vertex to Focus and Directrix to Vertex: | ||
| To get into Vertex form: | ||
| Focus in Vertex Form: | ||
| Directrix in Vertex Form: |