Quadratic equations

What does the quadratic formula represent?

The quadratic formula provides the solutions for the quadratic equation, defined by coefficients $a$, $b$, and $c$.

What is the discriminant in a quadratic equation?

The discriminant is given by $b^2 - 4ac$ and determines the nature of the roots of the equation.

What does a positive discriminant indicate about the roots?

A positive discriminant indicates that the quadratic equation has two distinct real roots.

What does a negative discriminant indicate about the roots?

A negative discriminant indicates that the quadratic equation has no real roots, only complex roots.

What does a zero discriminant indicate about the roots?

A zero discriminant indicates that the quadratic equation has exactly one real root, also known as a repeated root.

What is the vertex form of a quadratic equation?

Vertex form is an expression of a quadratic equation that allows easy identification of the vertex (peak or trough) of the parabola.

What is 'completing the square'?

Completing the square is a technique used to transform a quadratic equation into vertex form.

How does the leading coefficient affect a parabola?

The sign of the leading coefficient determines the direction in which the parabola opens; a positive sign indicates it opens upwards, while a negative sign indicates it opens downwards.

What is the purpose of factoring a quadratic equation?

Factoring helps to find the roots of a quadratic equation by identifying pairs of numbers that meet specified sum and product requirements.

What do we mean by 'roots' in a quadratic equation?

Roots are the solutions to the equation where the graph intersects the x-axis.