1. What is a Parabola in Vertex Form?

The vertex form of a parabola's equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola. This form clearly shows the vertex and how the parabola is stretched or compressed.

2. How Does the Calculator Work?

The calculator uses the vertex form equation:

Where:

• \( a \) — Determines the parabola's width and direction (up/down)
• \( h \) — X-coordinate of the vertex
• \( k \) — Y-coordinate of the vertex

Explanation: Given two points and the vertex, the calculator solves for 'a' and constructs the equation.

3. Importance of Vertex Form

Details: Vertex form is particularly useful for graphing as it immediately shows the vertex (the maximum or minimum point) and the parabola's axis of symmetry.

4. Using the Calculator

Tips: Enter coordinates for two points on the parabola and the vertex coordinates. The calculator will determine the 'a' coefficient and display the complete equation.

5. Frequently Asked Questions (FAQ)

Q1: What if my points don't lie on a parabola?
A: The calculator assumes valid input. If points don't fit a parabola with given vertex, results may be inaccurate.

Q2: Can I find the vertex with this calculator?
A: No, this calculator requires you to know the vertex. For finding vertex from points, use a different calculator.

Q3: What does the 'a' value represent?
A: 'a' determines the parabola's width and direction. Positive 'a' opens upward, negative opens downward. Larger absolute values make the parabola narrower.

Q4: Can I use this for horizontal parabolas?
A: No, this calculator only works for vertical parabolas (functions of x). Horizontal parabolas require x as a function of y.

Q5: How accurate are the results?
A: Results are mathematically precise for valid inputs. Rounding occurs only in display, not calculations.