math powerpoint- polynomial equations and graph of polynomial functions
TRANSCRIPT
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* A Mathematical expression that contains one or more terms. It is in the form of ax^n where a is a real number and n is a positive integer.
* an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
* a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.
Solve the equation. x4-20x2+64=0Solution:
x4-20x2+64=0
(x2)2 – 20 (x2) +64=0
(x2-16)(x2-4)=0
x2- 16=0 x2- 4=0
x2= 16 x2=4
x= ±4 x= ± 2
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Solve the equation. x5+10x3+9x=0Solution:
x5+10x3+9x=0x(x4-10x2+9)=0
x((x2)2-10(x2)+9)=0
x((x2-9)(x2-1))=0
x=0; x2-9=0; x2-1=0x=0; x2=9; x2=1x=0; x= ±3 x= ±1
* Graphing the polynomials only need the information of completing the list of all zeroes (including multiplicity) for the polynomial
* an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).
FIRST PROPERTY SECOND PROPERTY* There are no holes or breaks in the graph
and there are no sharp corners in the graph
* The graphs of polynomials will always be nice smooth curves.
* The “humps” where the graph changes direction from increasing to decreasing or decreasing to increasing are often called turning points
IF X=R IS A ZERO OF THE POLYNOMIAL P(X) WITH THE MULTIPLICITY K,
* If k is odd then the x-intercept corresponding to x=r will cross the x-axis
* If k is even then the x-intercept corresponding to x=r will only touch the x-axis and not actually cross it.
* Furthermore, if k>1 then the graph will flatten out at x=r
IF X=R IS A ZERO OF THE POLYNOMIAL P(X) WITH THE MULTIPLICITY K,
* If k is odd then the x-intercept corresponding to x=r will cross the x-axis
* If k is even then the x-intercept corresponding to x=r will only touch the x-axis and not actually cross it.
* Furthermore, if k>1 then the graph will flatten out at x=r
Graph the polynomial function:x3-2x2-3x
x F(x)
-3 -36
-2 -10
-1 0
0 0
1 -4
2 -6
3 0
4 20
* The degree of the polynomial is 3 and there would be 3 zeros for the functions.
* Make a table of values to find several points.
* Plot the points and draw a smooth continuous curve to connect the points
Graph the polynomial function:x2+x-12
x F(x)
-3 -6
-2 -10
-1 -12
0 -12
1 -10
2 -6
3 0
4 8
* Make a table of values to find several points.
* Plot the points and draw a smooth continuous curve to connect the points