94C Methods of Solving Quadratic Equations

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9-4C Methods of Solving Quadratic Equations
You will need a calculator for todays lesson.

• Adapted from Math 8H Completing the Square JoAnn
  Evans

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Solve by completing the square.
Keep everything except the constant on the left
side.
x2 6x 7 0
Leave a space for the number that will make a
perfect square trinomial. Whats half of -6,
squared?
x2 6x ___ -7
x2 6x 9 -7 9
Add 9 to both sides.
(half of -6)2
x2 6x 9 2 Simplify.
(x 3)2 2
Rewrite as a binomial squared.
Find the square root of each side.
Solve for x.
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Five ways of solving ax2 bx c 0
Find the Square Root---an efficient way to solve
ax2 c 0 Note there is no middle term.
Graphing---can be used for any quadratic, but
gives only approximate solutions.
Quadratic Formula---useful for any quadratic
gives exact solutions.
Factoring---an efficient way to solve IF the
equation is easily factored, which isnt always
the case.
Completing the Square---can be used for any
quadratic, but easiest when a is 1 and b is
an even number.
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White Board Practice
Round to the nearest tenth if necessary.
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Choose a method and solve the quadratic equation.
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Choose a method and solve the quadratic equation.
(half of 4)2
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Choose a method and solve the quadratic equation.
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Choose a method and solve the quadratic equation.
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Choose a method and solve the quadratic equation.
(half of 6)2
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Choose a method and solve the quadratic equation.
x equals negative b, plus or minus square root b
squared minus 4ac, all over 2a.
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Choose a method and solve the quadratic equation.
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Choose a method and solve the quadratic equation.
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Choose a method and solve the quadratic equation.
(half of -10)2
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Choose a method and solve the quadratic equation.
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Choose a method and solve the quadratic equation.
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Choose a method and solve the quadratic equation.
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Choose a method and solve the quadratic equation.
(half of -4)2
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Choose a method and solve the quadratic equation.
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Choose a method and solve the quadratic equation.
(half of -8)2
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Homework
9-A14 Handout A14.
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To solve a quadratic by Completing the Square,
follow these steps

• Make sure the coefficient of x2 is 1.

2. Move everything to the LEFT side of the
equation EXCEPT the constant.
3. Make the left hand side of the equation into
a PERFECT SQUARE TRINOMIAL.
4. Remember, if you add a number to one side of
an equation, you must add the same number to the
other side of the equation.
5. Factor the left side into the SQUARE OF A
BINOMIAL.
6. Take the square root of each side. Remember
to add the symbol to the right side.
7. Solve for x.