Chapter 6 - Algebra 2

Quadratic Functions, Completing the Square, Imaginary Numbers, Etc.

f(x)=a(x-h)²+k

f(x)=a(x-h)²+k

Vertex Form of Quadratic Function

x=h

Axis of Symmetry

(h, k)

Vertex

a < 0

Opens down, max

a > 0

Opens up, min

f(x)=ax²+bx+c

Standard Form of Quadratic Function

h= -b/2a

Finding h value from Quadratics

k= f(h)

Finding k value from Quadratics

(0, c)

y-intercept

a²-b² = (a+b)(a-b)

Difference of Squares

a²±2ab+b² = (a±b)²

Perfect Square Trinomial

i¹ equals…

i

i² equals…

-1

i³ equals…

-i

i⁴ equals…

1

a+bi/c+di = (a+bi/c+di)(c-di/c-di)

How to divide Complex Numbers

b²-4ac

Discriminant

b²-4ac > 0

2 real solutions

b²-4ac = 0

1 real solution

b²-4ac < 0

2 imaginary solutions

y=x²

Parent Function of a Quadratic

x= (-b±√b²-4ac)/2a

Quadratic Equation

c=(b/2)²

Find C value for Completing the Square