Algebra Chapter 10

1
Algebra Chapter 10

• 10.6
• Solving Quadratic Equations by
• the Quadratic Formula
• SPI Find the solution of a quadratic equation
  and/or zeros of a quadratic function.

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Your Purpose and Goals for today.

• Are to be able to solve quadratic equations using
  the quadratic formula.
• You all ready know how to solve quadratic
  equations by completing the square.
• You need to know how to use the quadratic formula
  so you can determine altitude of a rocket or
  determine how long a ball will stay in the air
  when thrown from a cliff.

3
Football.
Suppose a football player kicks a ball and gives
it an initial upward velocity of 47 ft/s. The
starting height of the football is 3 ft. If no
one catches the football, how long will it be in
the air?
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The Quadratic Formula
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Example 1 Solve
Substitute values for a, b, and c
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Example 2 Solve
Substitute values for a, b, and c
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Example 3 Solve
Substitute values for a, b, and c
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Example 4 Solve
Substitute values for a, b, and c Round
to the nearest hundredth.
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Vertical Motion
Object Dropped
Object Thrown Upward
Velocity can be positive (for an object moving
up, negative (for an object moving down), or zero
for an object that is not moving)
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Application problem Suppose a football player
kicks a ball and gives it an initial upward
velocity of 47 ft/s. The starting height of the
football is 3 ft. If no one catches the
football, how long will it be in the air?
Vertical motion formula
The football will be in the air for 3 seconds.
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Application problem From the top of a 40 foot
cliff, you throw a stone downward at 20 ft/sec
into the water below. How long will it take the
stone to hit the water?
Substitute values
The stone will hit the water in
approximately 1.08 seconds.
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Application problem Members of the science club
launch a model rocket from ground level with a
speed of 96 ft/s. After how many seconds will
the rocket have an altitude of 128 ft?
Substitute values Subtract 128 from both sides
The rocket is 128 ft above the ground after 2 s
and after 4 s.
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How long will a ball thrown upwards at 20
ft/sec stay in the air if it is thrown from a 100
ft. cliff?
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A building contractor..
Real life example of quadratic equations - A
building contractor was assigned to build a house
of floor area of1200 sq.ft with an instruction
that the length of the floor must be 10 ft more
than the width. What would be the floor
dimensions of the house?
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The contractor sets up an equation as, (l)(w)
1200 or (w 10)(w) 1200 or w2 10w â 1200
0 This is a quadratic equation in real life and
the roots are w -40 and w 30 The measure of
a width can not be negative and hence the
practical solution is w 30 and l 30 10
40. Thus the floor dimensions works out to 40ft
x 30 ft
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Reflection

• What is the quadratic formula?
• What are the specifics that you need to remember
  when using the quadratic formula to solve a
  quadratic equation.

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Extended Writing

• Tell what method you would use to solve the
  quadratic equation. Explain your choice or
  choices.

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OTL
p. 674-676 3-43 odd 46-48 all