Transcript 6.5 APPLICATIONS OF Quadratic Equations

APPLICATIONS OF
Quadratic Equations
STEPS:

1) Underline the key information.

2) Draw a diagram if necessary.

3) Assign the value of the unknown quantity
to “x”(or appropriate variable ex. t for time)
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4) Create a function “y”(or appropriate
variable) in terms of “x”.

5) Create a quadratic equation in terms
of “x” in standard form.

6) Solve the quadratic equation by
factoring or using the quadratic formula.
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7) If a maximum or minimum value is
required, solve using vertex form, not
using a quadratic equation.
EXAMPLES OF EACH TYPE OF
APPLICATION: Ex. 1: Integer
Question
The sum of the squares of two
consecutive even integers is 6052.
Determine the integers.
 SOLUTION:

...Example CONTINUED
Ex.2) Height with respect to
time

A football is thrown upward at an initial
velocity of 12m/s from a height of 1.5m
above the ground.
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a) Determine the equation of the height
of the ball.
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b) What is the height of the ball after 1s?
...Example CONTINUED
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c) After how many seconds does the ball
land?
...Example CONTINUED
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d) What is the maximum height of the ball
and when does this occur?
...Example CONTINUED
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e) When is the ball at a height of 1m?
...Example CONTINUED
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f) If the football was thrown on the
moon[g = 1.62 m / s],2 when would it hit
the ground?
Example 3: Area
Problem 3A: A rectangluar swimming
area at a beach is enclosed by a 240m
safety line on three sides. If the area of
m2
the swimming area is 6912
determine the length and the width of it.

...Example CONTINUED
Area

Problem 3B: A picture frame measures 40cm
by 75cm. A new frame is made by increasing
each side the same amount such that the area
of this new frame is 1.7 times the old one.
Determine the dimensions of the new frame to
the nearest tenth.
...Example CONTINUED
Example 4: Volume
An open topped box is to be constructed from
a square piece of cardboard by removing a
square with side length 8cm from each corner
and folding up the edges. The resulting box its
to have a volume of 512
3
cm dimensions
.
 Find the
of the original piece of
cardboard.

...Example CONTINUED
Example 5: Revenue
A ferry operator takes tourists to an island.
The operator carries an average of 500 people
per day for a round-trip fare of $20. The
operator estimates that for each $1 increase in
fare, 20 fewer people will take the trip.
 a) What fare will maximize the number of
people taking the ferry?

...Example CONTINUED
b) What price will provide a revenue
of $9520 per day?