What is a quadratic equation?

A quadratic equation is an equation that can be written in the form ax² + bx + c = 0, where a is not zero.

What is the quadratic formula?

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a). It can be used to solve any quadratic equation when a is not zero.

The discriminant is b² - 4ac. It determines whether a quadratic equation has two real roots, one repeated real root, or two complex roots.

When the discriminant is negative, the quadratic equation has two complex conjugate roots rather than two real roots.

A quadratic equation has the standard form:

ax² + bx + c = 0

where a, b, and c are numbers and a ≠ 0.

The roots of a quadratic equation can be found with the quadratic formula:

x = (−b ± √(b² − 4ac)) / 2a

The expression inside the square root is called the discriminant:

D = b² − 4ac

The value of the discriminant determines the type of roots:

Consider:

x² − 5x + 6 = 0

Here:

a = 1
b = −5
c = 6

The discriminant is:

D = (−5)² − 4(1)(6)
D = 25 − 24
D = 1

Since the discriminant is positive, there are two real roots:

x₁ = 3
x₂ = 2

For a quadratic function:

y = ax² + bx + c

the x-coordinate of the vertex is:

x = −b / 2a

Substitute this value into the original quadratic function to obtain the y-coordinate.