93A Solving Quadratic Equations by Finding Square Roots'

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9-3A Solving Quadratic Equations by Finding
Square Roots.
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
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You must learn how to use a calculator! There
are many makes and models. Read the instruction
booklet.
Enter a problem into the calculator for which you
already know the answer. For example

v
4
2
2
2nd
v
4

Keystrokes for TI-30X IIS
Keystrokes for TI-30X A
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Evaluate the expression. Give the exact value,
if possible. Otherwise, approximate to the
nearest hundredth. You may use a calculator
for this section.
Example 1
What is the positive square root of 8?
Example 2
What is the negative square root of 11?
Example 3
What is the positive and negative square root of
27?
hundredths
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Inverse Operations
Recall the use of inverse operations to solve
equations.
What is the inverse operation of addition? What
is the inverse operation of subtraction? What is
the inverse operation of multiplication? What is
the inverse operation of division? What is the
inverse operation of a square number?
The inverse of a square number is a square root.
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A quadratic equation is an equation that can be
written in the standard form
Quadratic equations can have one solution, two
solutions or no real solutions.
If b 0, the equation becomes
One way to solve a quadratic equation of this
form is to isolate the x2 on one side of the
equation. Then find the square root(s) of each
side.
Remember Squaring a number and finding the
square root(s) of a number are inverse operations.
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Solve the equation. Write the solutions as
integers if possible. Otherwise, round to the
nearest tenth.
How can you tell this is a quadratic equation?
Isolate the square term.
Undo the square by using square root.
Evaluate the radicals.
Do not give this answer!
One of the equations is not solved for a positive
variable! An equation is not considered solved
if the variable is negative. What do you get
when you undo the negative variable?
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Solve the equation. Write the solutions as
integers if possible. Otherwise, round to the
nearest tenth.
Isolate the square term.
Undo the square by using square root.
Evaluate the radicals.
Remember the variable cannot have a sign
because a negative variable is not solved.
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Solve the equations. Write the solutions as
integers if possible. Otherwise, round to the
nearest tenth.
Example 4
Example 5
Example 6
Remember the variable cannot have a sign
because a negative variable is not solved.
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Solve the equations. Write the solutions as
integers if possible. Otherwise, round to the
nearest tenth.
Example 7
Example 8
Example 9
Example 10
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Solve the equations. Write the solutions as
integers if possible. Otherwise, round to the
nearest tenth.
Example 7
Example 8
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Solve the equations. Write the solutions as
integers if possible. Otherwise, round to the
nearest tenth.
Example 9
Example 10
no real solution
Remember the variable cannot have a sign
because a negative variable is not solved.
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Solve the equations. Write the solutions as
integers if possible. Otherwise, round to the
nearest tenth. Remember a sign indicates two
solutions (roots).
Factor the P.S.T.
There are two solutions (roots)
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Solve the equations. Write the solutions as
integers if possible. Otherwise, round to the
nearest tenth.
Example 11
Example 13
Example 12
Example 16
Example 15
Example 14
Hint Isolate the squared term on one side of
the equal sign.
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Solve the equations. Write the solutions as
integers if possible. Otherwise, round to the
nearest tenth.
Example 11
Example 12
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Solve the equations. Write the solutions as
integers if possible. Otherwise, round to the
nearest tenth.
Example 14
Example 13
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Solve the equations. Write the solutions as
integers if possible. Otherwise, round to the
nearest tenth.
Example 16
Example 15
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Homework
9-A5 Pages 489 12-15 and Study Guide Page 20.