Quadratic Equations and Discriminants

Determining the discriminant

Simplifying the equation

Graphing the equation

Finding the roots

a^2 - 2ab + b^2

2a + 3b = c

b^2 - 4ac

a^2 + b^2 = c^2

Complex numbers

Real numbers

Imaginary numbers

Whole numbers

4

1

-4

0

One real root

Complex roots

Two real roots

No real roots

They are rational

They are irrational

They are equal

They are imaginary

Finding the vertex

Factoring the equation

Graphing the equation

Describing the nature of the roots

To determine the vertex

To describe the nature of the roots

To calculate the y-intercept

To find the axis of symmetry

x = a^2 + b^2

x = a + b + c

x = b^2 - 4ac

x = -b ± √(b^2 - 4ac) / 2a

4√15

3√20

√60

2√15