Algebra 2 Flashcards
Quadratic vertex form equation
y= a(x-h)^2+k
Quadratic vertex form AOS
x=h
Quadratic vertex form Vertex
(h, k)
Quadratic vertex form Y-int.
(0, plug in 0 and work out)
Quadratic standard form AOS
x= -b/2a
Quadratic standard form Vertex
(AOS, plug in AOS to equation and solve)
Quadratic standard form Y-int.
(0, C)
Quadratic standard form equation
y= ax^2+bx+c
Quadratic intercept form equation
y= a(x-p)(x-q)
Quadratic intercept form AOS
x= p+q/2
Quadratic intercept form Vertex
(AOS, plug in AOS to equation and solve)
Quadratic intercept form Y-int
(0, plug in 0 to equation and solve)
Quadratic intercept form X-ints.
(p,0)(q,0)
When both arrows point to Infinity
f(x)= AnX^even +….
When both arrows point to Negative Infinity
f(x)= -AnX^even +….
When Right arrow points Down and Left points Up
f(x)= AnX^odd +….
When Right arrow points Up and Left points Down
f(x)= -AnX^odd +….
limit notation
limf(x)= +/- infinity
x –> infinity
(RIGHT)
limf(x) = +/- infinity
x –> negative infinity
(LEFT)
Finding possible roots
Leading coefficient factors
Finding if roots are a solution
coefficients
(Root)
—————————————
bring down first coefficient under line then bring it above line and add with second coefficient. Bring that number down under line and multiply by root. Bring the multiplied number above line to add to next coefficient.
It is a solution if there is no remainder at the end.
Rational root theorem
(x-[root found as a solution]) (numbers under line as coefficients for the x’s)
note: x’s exponent gets a minus one.
Continue to simplify down and solve for x=
1 3 -4 -12 0
(x-[root])(x^3+3x^2-4x-12)
Reverse Rational Root Theorem
take x=numbers and plug into (x-__). fractions get toppled left. Ex: 1/3=(3x-1)
Multiply gogether to get the final equation.
