Solving%20Quadratic%20Equations%20by%20the%20Square%20Root%20Property

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Section 10.1
Solving Quadratic Equations by the Square Root
Property
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OBJECTIVES
Solve quadratic equations of the form
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DEFINITION
Square Root Property of Equations
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PROCEDURE
To solve any equation of form
Add B
Then
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PROCEDURE
To solve any equation of form
Divide by A
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PROCEDURE
To solve any equation of form
Using square root property,
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Section 10.1Exercise 1
Chapter 10 Quadratic Equations
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Solve.
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Section 10.1Exercise 2
Chapter 10 Quadratic Equations
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Solve.
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Section 10.1Exercise 3
Chapter 10 Quadratic Equations
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Solve.
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Section 10.1Exercise 4
Chapter 10 Quadratic Equations
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Solve.
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Solve.
or
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Section 10.1Exercise 5
Chapter 10 Quadratic Equations
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Solve.
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Section 10.2
Solving Quadratic Equations by Completing the
Square
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OBJECTIVES
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PROCEDURE

1. Find the coefficient of x term.

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PROCEDURE

1. Divide coefficient by 2.

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PROCEDURE

1. Square this number to obtain last term.

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PROCEDURE
Solving a Quadratic Equation by Completing the
Square

1. Write equation with variables in descending order
   on left and constants on right.

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PROCEDURE
Solving a Quadratic Equation by Completing the
Square

1. If coefficient of square term is not 1, divide
   each term by this coefficient.

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PROCEDURE
Solving a Quadratic Equation by Completing the
Square

1. Add square of one-half of coefficient of
   first-degree term to both sides.

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PROCEDURE
Solving a Quadratic Equation by Completing the
Square

1. Rewrite left-hand side as a perfect square
   binomial.

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PROCEDURE
Solving a Quadratic Equation by Completing the
Square

1. Use square root property to solve resulting
   equation.

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Section 10.2
Chapter 10 Quadratic Equations
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Section 10.2Exercise 6
Chapter 10 Quadratic Equations
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Section 10.2Exercise 7
Chapter 10 Quadratic Equations
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Section 10.2Exercise 8
Chapter 10 Quadratic Equations
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Section 10.2Exercise 9
Chapter 10 Quadratic Equations
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Section 10.3
Solving Quadratic Equations by the Quadratic
Formula
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OBJECTIVES
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OBJECTIVES
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DEFINITION
The Quadratic Formula
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DEFINITION
The Quadratic Formula
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DEFINITION
The Quadratic Formula
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DEFINITION
The Quadratic Formula
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Section 10.3Exercise 10
Chapter 10 Quadratic Equations
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Section 10.3Exercise 11
Chapter 10 Quadratic Equations
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Solve.
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Solve.
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Solve.
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Section 10.3Exercise 12
Chapter 10 Quadratic Equations
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Solve.
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Section 10.3Exercise 13
Chapter 10 Quadratic Equations
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Solve.
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Section 10.3Exercise 14
Chapter 10 Quadratic Equations
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Solve.
LCD 4
Multiply by 4
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Section 10.4
Graphing Quadratic Equations
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OBJECTIVES
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OBJECTIVES
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DEFINITION
Graph of a Quadratic Equation
The graph of y ax2 bx c is a parabola that
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PROCEDURE
Graphing a Factorable Quadratic Equation

• Find y-intercept by letting
• x 0, then finding y.

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PROCEDURE
Graphing a Factorable Quadratic Equation

• Find x-intercept by letting
• y 0, factoring equation
• then solving for x.

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PROCEDURE
Graphing a Factorable Quadratic Equation

1. Find vertex by averaging solutions of equation
   and substituting in equation to find
   y-coordinate.

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PROCEDURE
Graphing a Factorable Quadratic Equation

1. Plot points found and one or two more points.

Curve drawn through points found is graph.
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Section 10.4Exercise 15
Chapter 10 Quadratic Equations
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turns up
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Section 10.4Exercise 16
Chapter 10 Quadratic Equations
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turns up
so
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Section 10.4Exercise 17
Chapter 10 Quadratic Equations
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turns down
so
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Section 10.4Exercise 18
Chapter 10 Quadratic Equations
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Section 10.5
Applications Pythagoras Theorem
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OBJECTIVES
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OBJECTIVES
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DEFINITION
Pythagorean Theorem
Square of hypotenuse of a right triangle equals
sum of squares of other two sides
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Section 10.5Exercise 19
Chapter 10 Quadratic Equations
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Find the length of the hypotenuse of a right
triangle if the lengths of the two sides are 2
inches and 5 inches.
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Section 10.5Exercise 20
Chapter 10 Quadratic Equations
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Section 10.6
Functions
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OBJECTIVES
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OBJECTIVES
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OBJECTIVES
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DEFINITIONS
Relation, Domain and Range
A relation is a set ofordered pairs.
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DEFINITIONS
Relation, Domain and Range
Domain of a relation is the set of all possible
x-values.
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DEFINITIONS
Relation, Domain and Range
Range of relation is the set of all possible
y-values.
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DEFINITION
Function
Set of pairs in which each domain value has
exactly one range value.
(no two different ordered pairs have same first
coordinate)
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Section 10.6Exercise 21
Chapter 10 Quadratic Equations
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Find the domain and range of
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Section 10.6Exercise 22
Chapter 10 Quadratic Equations
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Find the domain and range of
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Section 10.6Exercise 23
Chapter 10 Quadratic Equations
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State whether each of the following is a function.
This is not a function.
This is a function.
(For every x, unique y)
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Section 10.6Exercise 24
Chapter 10 Quadratic Equations
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Section 10.6Exercise 25
Chapter 10 Quadratic Equations
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The average price P(n) of books depends on the
number n of millions of books sold and is given
by the function
Find the average price of a book when 20 million
copies are sold.
The average price is 17.