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Finding Zeros in Polynomial Functions - Coggle Diagram
Finding Zeros in
Polynomial Functions
Quadratic
Given Graph
look at the x-axis and
find intersection points
no intersection points
2 imaginary roots, would have
to use calculation (writing
equation in any form and solving)
1 intersection point
intersection point = root
find 1 solution
2 intersction points
intersection point = root
Given Equation
Standard Form
(set y=0)
Quadratic Formula
Calculate x
Factoring
completing the square
Intercept Form
x-intercepts are given
f(x)=a(x-p)(x-q),
where p and q are roots
Vertex Form
directly calculate
y=a(x – h)^2 + k
Given point and Vertex
solve by
writing formula
substitute point
to vertex form
y=a(x - vertexx)^2 + vertexy
Linear
point-slope form
y-y₁=m(x-x₁)
substitute y=0
standard form
ax+by=c
given graph
check y=0 line
Cubic
given graph
chek the line y=0 for intersection points
given equation
P/Q method
P is a set of all factors of a, postive or negative
Q is a set of all factors of b, postive or negative
P/Q is a set of all possibel P/Q values, postive or negative
and test out possible P values
synthetic devision:
lay out the coefficients of the function in order
put a line on the left of the laid out numbers
put a line below the numbers, leaving a 1-line gap
drop down the first term to below the line
multiply the bottom by the supposed zero, add it to the middle of next column
add the top with the middle to get the bottom
repeat 5 and 6 until last term
last bottom term is remainer
test out a series of P/Q to get factors
Degree 4+
factor out to possibly make it
into a smaller degree function times x^n
*additional zero of 0
given grpah
look at graph and determine
Grouping
Jeff method: Breaking middle terms to create a situation that is possible for direct grouping
Directly group: find terms that
have a gcf and group to find factors
further broken into less degree