PreCalc Quad Applications
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Transcript of PreCalc Quad Applications
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2.1 Continued: Quadratic
ApplicationsObjectives:
1. Review the three forms of quadratics and how they areused
2.) Be able to find the vertex of the parabolas and x-intercept(s) regardless of form and APPLY to projectile
motion functions
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Page 125
If f is a polynomial function and r1 is a realnumber , the following statements areequivalent/ synonomous
x= r1 is a zero of the function f.
x = r1 is a solution of the polynomial equation f(x)= 0
(x r1) is a factor of the polynomial f(x)
(r1, 0) Is an x-intercept of the graph of f(x)
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Factored Form
Quadratics
y = a(x r1)(x r2)
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Analyzing Graphs What are the values of x where the graph
crosses the x-axis?
Roots?
X-intercepts?
Factors?
Factored Form?
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What are the values of x where the graph
crosses the x-axis?
Analyzing Graphs
Roots?
X-intercepts?
Factors?
Factored Form?
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Graph the function y = (x 2)(x 5)
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Bouncers/ Double roots
Squares are bounced
(x -1)2
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Bouncers/ Double roots
Squares are bounced
(x -1)2
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Double roots bounce off of the x-axis
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Sketch the graph of
f(x)= -(x-3)2
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Application of Quadratics
Projectile Motion Function
h(x) = ax2 + bx + c a function of height with
respect to time
a = acceleration of gravity
a= -4.9 m/sec2
a = -16 ft/sec2
b = initial velocity in which object was thrown
c= initial height
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Stephen throws a ball up from his waist level
at 1 meter above the ground. He throws it atthe speed of 18 m/s and means to catch it, but
he misses and it falls to the ground.
a.) When does the ball hit the ground? After
how many seconds?
b.) What is the maximum height reached byMitchs ball?
c. When does the ball pass the point from
which it was released?
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Application of Quadratics
Area Problems
A(x) = width 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 commonsense?
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Applications of quadratics
I am building a fenced in area for my dog Aldo that is attached tomy garage. If I have 40 feet of fencing, what should my dimensionsbe to maximize the area? Write it as a function with respect to w.
Use perimeter equation to writean area equation in terms of just one
variable
Find the factor of the quadratic equation
you created.
Garage
w
w
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Other Maximization Problems
#80
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Homework
Packet and Pg. 118 #75; 76-80(ev)
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Chapter 9.2
Review the unit circle
Review radians vs. degrees
Review the six trigonometric functions