All posts by eval2014

[Week 9]- Analyzing Quadratic Functions of the Form

[Week 9]- Analyzing Quadratic Functions of the Form

What did I learn:

  1. Determine the characteristics of the graph of a quadratic function form its equation in standard form and sketch the graph.
  2. Determining an equation of quadratic function form its graph.
  3. Graphing a quadratic function with its equation in standard form.
  4. Determining an equation of a quadratic function using its characteristics.
  5. Using the equation of a quadratic function to model a situation.
  6. Complete the square to write an equation in general form as an equation in standard from.
  7. Determine the characteristics of the graph of a quadratic function with its equation in general form.

Ex.1

 

EX.2

[Week 8]- Properties of a Quadratic Function

[Week 8]- Properties of a Quadratic Function

What did I learn:

  1. Determine the characteristics of a quadratic function and sketch its graph.
  2. Identifying the characteristics of a Quadratic function form its graph.
  3. Identifying quadratic functions using first differences.
  4. Graphing a quadratic function that models a situation.
  5. Relate a quadratic equation to its corresponding quadratic function.
  6. Explore three transformations of the graph of a quadratic function.

Ex.1

Ex.2

[Week 6]-Developing and applying the quadratic formula

[Week 6]-Developing and applying the quadratic formula
What I have learned:
Solving quadratic equations by determining square roots.
Solving by completing the square when a=1.
Solving by completing the square when a≠1.
Solving a problem using a quadratic equation.
Solving a quadratic equation of the form x^2+bx+c=0 .
Solving a quadratic equation of the form ax^2+bx+c=0 .
Using the quadratic formula to solve a problem.

Ex. Solve equation. Verify the solution.
2x^2-1=5
2x^2-1=5 Isolate the x^2-term.
2x^2=6 Divide each side by 2
x^2=3 Take the square root of each side.
X= ±√3
To verify, substitute each root in the given equation 2x^2-1=5 .
For x=√3,
L.S.= 2(√3)^2-1
=5

For x=-√3,

$ latex L.S.=  2(-√3)^2-1 $

=5
For each root, the left side is equal to the right side, so the solution is verified.

 

 

 

[Week 5]- Factoring Polynomial Expressions

[Week 5]- Factoring Polynomial Expressions
What I have learn:
Determining whether a given binomial is a factor of a given trinominal.
Factoring trinomials with rational coefficients
Factoring using a trinomial pattern.
Factoring using the difference of squares pattern.

Ex. Is d-4 a factor of each trinomial? Justify the answer.
2d^2+6d-56
Use logical reasoning.
If d-4 is a factor, then trinomial can be written as:
(d-4) (ad+b)
2d^2+6d-56 = (d-4) (ad+b) Expand
2d^2+6d-56 = ad^2-(4a+b)d-4b
The d^2 – terms on both sides must be equal.
a=2
-4b= -56,
So b= 9
The trinomial would be: (d-4)(2d+9)
Expand to check the d- term.
(d-4)(2d+9) = 2d^2+6d-56
since this trinomial is equal to the given trinomial, d-4 is a factor of the given trinomial.

[Week 4]- Multiplying and Dividing Radical Expressions

[Week 4]- Multiplying and Dividing Radical Expressions

What I have learned:

  1. Adding and Subtracting Radical Expressions
  2. Simplifying with more than one set of like terms
  3. Multiplying and dividing radical expressions
  4. simplifying products of expressions with variable radicands
  5. Rationalizing a monomial denominator

 

Ex. Simplify √63+√40-√90-√28

The radicals are different, so simplify each radical.

√63+√40-√90-√28

= 3√7+2√10-3√10-2√7
= 3√7-2√7+2√10-3√10
= √7-√10

Ex. Simplify 2√x-3√y+5√x+2√y; x,y,≥0

2√x and 5√x are like terms because they are radicand x and index 2.
3√y and 2√y are like terms because they have radical y and index 2.

2√x-3√y+5√x+2√y
= 2√x+5√x-3√y+2√y
= 7√x-√y

Ex. Expand and simplify(2√3+5)(2√3-5)

Expand

(2√3+5)(2√3-5)
= (2√3)(2√3)-5*5
= 12- 25
= -13

 

 

[Week 3]- Absolute value of a real number

[Week 3]- Absolute value of a real number

What I have learned:

  1. What is the absolute value of a real number
  2. The absolute value of a real number is defined as the principal square root if the square of a number.
  3. Determine absolute value.
  4. The relationship with absolute and principal square root.
  5. √x ² = |x|

 

Ex. Determine each absolute value.

|4.2|, |-6.1|, |0|, | -3/4 |

4.2, 6.1, 0, 3/4

 

Ex. Evaluate√(3-5) 2

          Use the fact that √(3-5)2  =  |x|

√(3-5)2 = |3-5|

                                             = |-2|

= 2

[Week 2]- Geometric Series

[Week 2]- Geometric Series

What I have learned:

  1. The sum of n terms of a geometric series
  2. Use a rule to determine the sum of n terms of a geometric series, then solve related problems.
  3. Use a rule to determine the nth term in a geometric sequence.
  4. Use a rule to determine any of n, t1, tn, or r in a geometric sequence.
  5. Use a rule to determine n and Sn in geometric series, given the values of r, n, or Sn.

Ex. Find the S15 of the sequence -5, 10, -20…

Ex. Find the n of the sequence 1-2+4-8+…-512

[Week 1]- Arithmetic Sequences

[Week 1]- Arithmetic Sequences

What I have learned:

  1. what is arithmetic sequences and common different.
  2. How to find common different.
  3. How to calculate the sum of n term of an arithmetic series
  4. Use a rule to determine t1 and d in an arithmetic sequence given the values of tn and n.
  5. Use a rule to determine tn and n in an arithmetic sequence given the values of t1 and d.
  6. Use a rule to determine the sum Sn of an arithmetic series.

 

Ex. Use the arithmetic series, determine the indicated value.

1 + 3.5 + 6 + 8.5 + …; determine S42.

Know:                                     Sn = n/2 [2 t1 + d (n-1)]

T1 = 1                                           = 42/2[2+2.5*41]

T2= 3.5                                         = 2194.5

d= 2.5

 

 

Ex. Use the giving data to determine the indicated value.

S20 = -850 and t20 = -90; determine t1

Sn = n/2 (t1 +tn)

-850 = 20/2[t1 +(-90)]

10 t1 = 50

t 1 = 5