1. What is Standard Form of a Quadratic Equation?

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are coefficients and a ≠ 0. This form is essential for solving quadratic equations using various methods like factoring, completing the square, or the quadratic formula.

2. How Does the Calculator Work?

The calculator converts given coefficients into the standard form:

Where:

• \( a \) — Coefficient of x² (must not be zero)
• \( b \) — Coefficient of x
• \( c \) — Constant term

Explanation: The calculator properly formats the equation with appropriate signs and omits coefficients when they equal 1 or -1 for cleaner presentation.

3. Importance of Standard Form

Details: The standard form is crucial for identifying key properties of quadratic equations, including the direction of opening, axis of symmetry, vertex, and y-intercept. It's also the preferred form for applying the quadratic formula.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c. The coefficient a must be non-zero. The calculator will format the equation properly, handling positive and negative coefficients appropriately.

5. Frequently Asked Questions (FAQ)

Q1: Why must coefficient a not be zero?
A: If a = 0, the equation becomes linear (bx + c = 0), not quadratic. Quadratic equations must have a degree of 2.

Q2: Can I use fractions or decimals as coefficients?
A: Yes, the calculator accepts decimal inputs. For fractions, you may need to convert them to decimal form first.

Q3: What if my equation is not in standard form?
A: This calculator helps convert any quadratic equation to standard form by organizing the terms in descending order of exponents.

Q4: How does the calculator handle negative coefficients?
A: Negative coefficients are properly displayed with minus signs in the appropriate positions in the equation.

Q5: Can this calculator solve the equation too?
A: No, this calculator only converts to standard form. You would need a quadratic equation solver to find the roots.