1. What Is A Quadratic Equation?

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a, b, and c are coefficients and a ≠ 0. It represents a parabola when graphed on a coordinate plane.

2. How Does The Calculator Work?

The calculator converts quadratic equations to standard form:

Where:

• \( a \) — Coefficient of x² (must be non-zero)
• \( b \) — Coefficient of x
• \( c \) — Constant term

Explanation: The calculator takes the input coefficients and formats them into the standard quadratic equation form with proper sign handling.

3. Importance Of Standard Form

Details: The standard form ax² + bx + c = 0 is essential for identifying coefficients, calculating the discriminant, finding roots using the quadratic formula, and analyzing the parabola's properties.

4. Using The Calculator

Tips: Enter the coefficients a, b, and c as real numbers. Coefficient a must be non-zero. The calculator will display the equation in proper standard form with correct signs.

5. Frequently Asked Questions (FAQ)

Q1: Why must coefficient a be non-zero?
A: If a = 0, the equation becomes linear (bx + c = 0) rather than quadratic, as it loses its second-degree term.

Q2: What if coefficients b or c are zero?
A: The calculator properly handles zero coefficients by omitting the corresponding terms from the standard form representation.

Q3: Can I use fractions or decimals as coefficients?
A: Yes, the calculator accepts both integer and decimal inputs for coefficients a, b, and c.

Q4: What is the quadratic formula?
A: The quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) is used to find the roots of a quadratic equation in standard form.

Q5: How does standard form help in graphing?
A: The standard form reveals the parabola's direction (based on a's sign), y-intercept (c), and helps find the vertex using \( x = -\frac{b}{2a} \).