precalc quad applications

8/2/2019 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

precalc quad applications

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