Quadratics/ Rationals

What is the discrimanent?

b²-4ac

How do you find the Vertex?

-b/2a

Maximum

When a parabola is negative

Minimum

When a parabola is positive

Vertical Asymptotes

When the denominator= 0

Holes

when there is a common factor

X-Intercepts

when the numerator= 0

Y-intercept

f(0)

Degree of numerator < denominator

Horizontal asymptote at y=0

degree of numerator = denominator

horizontal asymptote at y= the ratio of the leading coefficients

Degree of numerator > denominator

Polynomial long division- limits are infinity/ negative infinity depending on 9 basic functions

Standard form

y=ax²+bx+c

Vertex form

Y=a(x-h)²+k

Factored form

y=a(x-p)(x-r)

Discriminant= 0

One rational solution

Discriminant< 0

Two imaginary solutions

Discriminant > 0

Two irrational solutions

Discriminant = perfect square

Two rational solutions