Quadratic Equation Solver
Solving Quadratic Equations
A quadratic equation is a second-degree polynomial equation of the form \(ax^2 + bx + c = 0\), where 'a' is not zero. The solutions to this equation are called roots.
The Quadratic Formula
The roots are found using the quadratic formula:
\[ x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} \]
The Discriminant (\(\Delta\))
The part of the formula under the square root, \(\Delta = b^2-4ac\), is called the discriminant. It determines the nature of the roots:
- If \(\Delta > 0\), there are 2 distinct real roots.
- If \(\Delta = 0\), there is exactly 1 real root.
- If \(\Delta < 0\), there are 2 complex roots.
Parabola Properties
The graph of a quadratic function is a parabola.
Vertex: \( \left( -\frac{b}{2a}, f(-\frac{b}{2a}) \right) \)
Axis of Symmetry: \( x = -\frac{b}{2a} \)
Solves \(ax^2 + bx + c = 0\) and graphs the parabola.
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