Vertex Form Converter
How It Works
This vertex form converter uses established formulas to provide accurate results.
The basic rule:
- Standard form: ax² + bx + c
- Vertex form: a(x - h)² + k
- h = -b/(2a), k = c - b²/(4a)
- Axis of symmetry: x = h
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
What is the difference between standard and vertex form?
Standard form ax²+bx+c is best for finding roots and the y-intercept. Vertex form a(x-h)²+k is best for identifying the vertex, axis of symmetry, and graphing. Both represent the same parabola.
How do I convert vertex form back to standard form?
Expand the squared term: a(x-h)² + k = a(x²-2hx+h²) + k = ax²-2ahx+ah²+k. This gives standard form with b=-2ah and c=ah²+k.
How does 'a' affect the parabola?
If a > 0, the parabola opens upward. If a < 0, it opens downward. Larger |a| makes it narrower (steeper), smaller |a| makes it wider (flatter).