A quadratic equation is a second-degree polynomial equation that can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants.

A linear equation having only one variable.

A polynomial equation with three variables: ax^2 + bx + c = 0.

An equation in the form bx + c = 0.

ax^2 + bx + c = 0.

ax^2 + c = 0.

ax^2 + bx = 0.

x^2 + bx + c = 0.

The color of the graph.

The direction and width of the parabola; if 'a' is positive, the parabola opens upward, and if negative, it opens downward.

It affects the value of 'b' in the equation.

The texture of the graph.

x = (-b ± √(b^2 - 4ac)) / (2a), used to find the roots of a quadratic equation.

x = (bx + c) / a.

x = a^2 + b^2 - 4ac.

x = b ± √(b^2 - 4ac).

They are the leaves of a mathematical tree.

They are complex numbers.

The roots of the equation are the solutions or values of x that satisfy the quadratic equation.

They denote the coefficients in the equation.

By checking the parity of the numbers involved.

By solving the equation twice.

By calculating the discriminant (b^2 - 4ac); if it's positive, there are two roots, if zero, one root, and if negative, no real roots.

By looking at the coefficients of the equation only.

It is the integer part of the root of an equation.

It is the sum of coefficients.

A measure of the slope of the roots.

The discriminant is the part of the quadratic formula under the square root: b^2 - 4ac. It indicates the nature of the roots.

A process of adding coefficients.

It's a method to integrate constants.

Factoring is a method to simplify a quadratic equation by expressing it as a product of its linear factors.

Approximating the value of the solution.

Quadratic equations with two real roots.

Perfect square trinomials are quadratic equations that can be factored into a binomial squared. They take the form (ax + b)^2.

Equations that do not factor easily.

Expressions that are perfect squares of constants.

Completing the square is a method to solve quadratic equations by converting them into a perfect square trinomial.

A method for finding complex roots.

The process of finding zeros of linear equations.

A technique to approximate roots by graphic representation.

It forms a straight line.

It creates a circle.

A quadratic equation graph is a parabola, a U-shaped curve that can open up or down depending on the coefficient of x^2.

It forms a zigzag pattern.

The intersection point of the parabola with the x-axis.

The vertex is the highest or lowest point of the parabola, depending on its orientation, and can be found at (-b/(2a), f(-b/(2a))).

The point where the parabola meets the y-axis.

The midpoint of the parabola.

Solve by graphing the equation and locating the x-values (roots) where the parabola intersects the x-axis.

By counting the number of peaks in the graph.

By finding the midpoint of the parabola.

Solving using tangent lines to the graph.

A horizontal line that runs through the root of the equation.

The axis of symmetry is a vertical line that divides the parabola into two mirror images, given by x = -b/(2a).

A diagonal line that crosses the parabola at the vertex.

A horizontal line through the focus of the parabola.

Real roots have non-imaginary values and appear on the x-axis; complex roots involve imaginary numbers when the discriminant is negative.

All roots are complex and have negative parts.

Real roots have imaginary parts while complex roots are whole numbers.

Complex roots always turn into real numbers upon solving.