1. What is Factored to Standard Form Conversion?

The calculator converts a quadratic equation from its factored form \((x - r_1)(x - r_2)\) to the standard form \(ax^2 + bx + c\). This is useful for analyzing quadratic functions and solving equations.

2. How Does the Calculator Work?

The calculator uses the mathematical identity:

Where:

• \( r_1 \) — First root of the quadratic equation
• \( r_2 \) — Second root of the quadratic equation
• The resulting standard form is \( x^2 + bx + c \)

Explanation: The calculator expands the product of two binomials to produce a quadratic trinomial in standard form.

3. Importance of Quadratic Forms

Details: Standard form is essential for identifying the coefficients used in the quadratic formula, analyzing parabolas, and finding the vertex of the quadratic function.

4. Using the Calculator

Tips: Enter the two roots of the quadratic equation. The calculator will automatically compute the standard form coefficients.

5. Frequently Asked Questions (FAQ)

Q1: What if my roots are complex numbers?
A: This calculator works with real roots only. For complex roots, the standard form would have complex coefficients.

Q2: Can I use this for quadratics with a leading coefficient other than 1?
A: This calculator assumes a leading coefficient of 1. For other cases, you would need to multiply through by the leading coefficient.

Q3: How is this related to the FOIL method?
A: This calculation is essentially applying the FOIL (First, Outer, Inner, Last) method to multiply the two binomials.

Q4: What if I have a double root?
A: Simply enter the same value for both roots (perfect square trinomial case).

Q5: Can I convert from standard form back to factored form?
A: This would require factoring the quadratic, which is only possible when the discriminant is non-negative.