Quadratic Equations
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)
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.
7) If a maximum or minimum value is
required, solve using vertex form, not
using a quadratic equation.
APPLICATION: Ex. 1: Integer
The sum of the squares of two
consecutive even integers is 6052.
Determine the integers.
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Ex.2) Height with respect to
A football is thrown upward at an initial
velocity of 12m/s from a height of 1.5m
above the ground.
a) Determine the equation of the height
of the ball.
b) What is the height of the ball after 1s?
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c) After how many seconds does the ball
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d) What is the maximum height of the ball
and when does this occur?
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e) When is the ball at a height of 1m?
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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
the swimming area is 6912
determine the length and the width of it.
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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.
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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
cm dimensions
 Find the
of the original piece of
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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?
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b) What price will provide a revenue
of $9520 per day?

6.5 APPLICATIONS OF Quadratic Equations