Pre-Calc 2.1[1]
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Transcript of Pre-Calc 2.1[1]
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By: Brooke Tellinghuisen
Kelli Peters
Austin Steinkamp
Chapter 2 Section 1
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TermPolynomials
Degree
Leading
coefficient
2x-2
2562234 xxx
246324
xxx
2253
xx
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012
2
1
1... aaaaaf
n
n
n
n!
Example of Polynomial Functions
Polynomials are classified by degree.
Formula of Polynomial Function
baxxf ! cxf !
2
xxf !
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2nd degree polynomials functions are called quadraticfunctions.
Example of Quadratic Functions
Formula of Quadratic Function
NOTE: a, b, and c are real numbers with a 0.
1
31
6
!
!
!
xxxf
xxf
xxxf
cbxaxxf ! 2
{
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a
acbb
2
42s!
Used to find zeros (roots) in a
quadratic function.
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The graph for a quadratic function is a U-shaped
graph, called a parabola.
If the leading coefficient is positive, the graph opens
upward.
If the leading coefficient is negative, the graph opens
downward.
0, "! acbaf
0, ! acbaf
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The point where the axis intersects the parabola is the
vertex.
If a > 0, the vertex is the point with the minimum y-
value on the graph.
If a < 0, the vertex is the point with the maximum y-
value on the graph.
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F(x)=(x-2)^2
Tell what direction the graph moves and if it
opens up or down.
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Since the 2 is connected with the x in the parentheses the graph
moves the opposite way of what u think it would. Since its a
subtraction problem it moved to the right.
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Find the vertex and x-intercepts of the equation
f(x)=x2-5
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Take (x2-5) and set equal to zero
x2-5=0
+5 =+5
x2 =5
5s!x
To find your vertex
Those would be your
x-intercepts
a
bf
a
b
2,
2
Use the formula to find
your vertex
)(2
Plug 0 back into
the equation and
solve.Your answer is (0, -5)
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Area Problem
A(x)=width x length
A farmer has 200 yards of fencing. Write the area
as a function of x, if the farmer encloses a
rectangular area letting the width equal to x.
What is my maximum area? What are my zeros?
Do the zeros match common sense?
L
XX
L
2x+2L=200
-2x -2x
2L=200-2x
2L/2=200-2x/2
L=100-x
X-100=x(-x)
-x2+100x
Finding the Vertex
-100/ 2(-1)
(50,2500)
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An object is launched at 19.6 meters per second
from a 58.8 meter tall platform.
The equation for the objects highest s at time t
seconds after launch is s(t)=-4.9t2+19.6t+58.8,where s is in meters.
When does the object strike the ground?
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0=-4.9t2+19.6t+58.8
0=t2-4t-12
0=(t-6)(t+2)
So T=6 and -2. The answer cant be negative so
the object hit the ground at 6 seconds after the
launch.