Quadratic Equations

A quadratic equation is a polynomial equation of degree 2. The standard form is:

$ax^2 + bx + c = 0$

Where $a$ , $b$ , and $c$ are constants and $a \neq 0$ . The graph of a quadratic function is a U-shaped curve called a parabola.

There are three main methods to solve quadratic equations:

Factoring: Converting the equation into $(x-p)(x-q)=0$ form.
Completing the Square: Transforming the equation into $(x+d)^2 = e$ .
Quadratic Formula: Using the formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ .

Interactive Visualizer

Adjust the coefficients $a$ , $b$ , and $c$ to see how they change the shape and position of the parabola.

The Vertex Form of a quadratic equation is useful for finding the maximum or minimum point of the parabola:

$y = a(x - h)^2 + k$

Where $(h, k)$ is the vertex.

Step-by-Step Solution0 / 3 Problems

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