[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.
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:
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:

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

√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