What is a quadratic equation?
An equation of the form ax² + bx + c = 0, where the highest power of x is 2. Its graph is a parabola, a smooth U-shaped (or ∩-shaped) curve.
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Quadratic equation solver
Real and complex roots of ax² + bx + c = 0.
x = (−b ± √(b²−4ac)) / 2a
Frequently asked questions
What is the quadratic formula?
x = (−b ± √(b² − 4ac)) / 2a. The ± gives the two possible solutions, which are the points where the parabola crosses the x-axis.
What does the discriminant tell me?
The discriminant is b² − 4ac. If it is positive there are two real roots; if zero, one repeated root; if negative, no real roots — the parabola never touches the x-axis and the roots are complex.
Where is this used in real life?
Projectile paths — the height of a thrown ball over time is a quadratic, and the roots tell you when it lands. Area problems — finding a rectangle's dimensions from its area and perimeter. Business — profit models that rise then fall, where the roots mark break-even points and the vertex marks maximum profit.
How does the parabola graph help?
The curve shows the roots as the points where it crosses the x-axis and the vertex as its turning point, so you can see at a glance how many real solutions the equation has.