Week 8 blog post 4.1 Properties of a Quadratic Function

Posted on April 15, 2018 by hanluq2015

Ms Burton, I learned this chapter on Youtube by myself. And I took some notes.

The vertex of a parabola is its highest or lowest point.(_,_) The vertex may be a maximum or minimum point.

If the graph opens up, x should be positive, the vertex amy be the minimum point, the domain can be any real numbers, and the range must be y>= (greater than the vertex)

If the graph opens down,x should be negative, the vertex amy be the maximum point, the domain still can be any real numbers, and the range must be y<= (lease than the vertex)

Week 7 Developing and Applying the Quadratic Formula

Posted on March 16, 2018 by hanluq2015

When we solve this kind of questons, we need to follow the steps and check carefully after his work. We need to calcuate again and compare our work to his work, that helps find the mistakes.

(PS: Ms Burton, hope you enjoy your wonderful spring break 🙂 )

Week 6 Developing and Applying the Quadratic Formula

Posted on March 11, 2018 by hanluq2015

$x^2$ – 6x + 4=0

For me, quadratic formula is the easiest problem to solve because the only way to solve this is to remember the formula, and put each pattern in the foumula. Firstly, we need to find a, b and c for this formula in this question. A = 1, b= -6, c=4. Secondaly, is to find the formula: $x={\frac {-b\pm {\sqrt {b^{2}-4ac}}}{2a}}.$ . Finally, place each pattern in the formua.

We can get that: The next important thing is that: do not forget to simplify (if it is possible) the last answer.

Week 5 Factoring Polynomial Expressions

Posted on March 3, 2018 by hanluq2015

$x^2$ -11x +30

=(x-5) (x-6)

Before solving this type of question, we should remind ourselves of the ‘CDPEU’ chart, then find the right direction for solving this kind of question. According to the chart, this question is a trinomial one. The first part( $x^2$ ) and the last part(30) always provides informtaion. For example, if we want to find the factor of this one, we need to look at the first part and the last part. The last part is 30. 30=3 × 10=2×15=5×6, the middle part is -11x. Due to -11, we can eliminate 3&10, 2&15 becasue regardless of adding or substracting, 3&10 or 2&15 still can not get the answer of 11. There is only answer: 5&6 becasue 5+6=11, but there is one thing very important is that the number is -11(it’s negative). The last part is a postive 30, so the final answer is -5&-6.

Week 4 Multiplying and Dividing Radical Expressions

Posted on February 25, 2018 by hanluq2015

Expand and simplify: (P127)

a) ( $\sqrt{3}$ +8) ( $2\sqrt[1]{3}$ -1) – $\sqrt{3}$ ( $7\sqrt[1]{3}$ -4)

=6- $\sqrt{3}$ + $16\sqrt[1]{3}$ -8-(21- $4\sqrt[1]{3}$ )

=-2 + $15\sqrt[1]{3}$ -21 + $4\sqrt[1]{3}$

=-23+ $19\sqrt[1]{3}$

Firstly, when we solve this type of questions, we need to find the like terms becasue when adding/ substraction, the coefficients are combined when the radicands are the same. For example, in this question, like terms are $\sqrt{3}$ , $2\sqrt[1]{3}$ and $\sqrt{3}$ ( $7\sqrt[1]{3}$ becasue you can find they all have $\sqrt{3}$ , and that means we need to think of a way to combine them together to get a simplified answer. Secondly, do the calculation carefully and be aware of the like terms. Final step is to check you answer is already simplified or not.

Week 3 Simplifying Radical Expressions

Posted on February 17, 2018 by hanluq2015

3: Write each mixed radical as an entire radical (page 100)

– $2\sqrt[3]{5}$

= $\sqrt{-40}$

When I first do this question,I was confused by the difference of the mixed radical and entire radical. I think the most difficult part is the index part becasue there is a tube and I don’t know how to solve this. And we only learned how to simplify in Grade 10. My understanding is that when we solve this type of question, we need to multiple all the numbers outside the root, the index and so as the radicand together. When there is a tube (3), just multiple 3, we don’t have to multiple three times becasue that’s not the exact meaning of tube. The most important thing is that we should be careful when we do the calculating.

Week 2 Geometric Sequence

Posted on February 13, 2018 by hanluq2015

Determine $S_{10}$ for each geometric series. Give the answer to 3 decimal places. (page 49)

a)0.1+ 0.01+ 0.001+ 0.0001+…

know: $t_{1}$ =0.1 ( $t_{1}$ means the first one, the first place)

r=0.1( 0.01 divided by 0.1)( each term is multiplied by a constant known as the common ratio) ( to determine the common ratio, divide any term by the preceding term)

n=10 ( a nautral number and menas the term , for instance, as the question asks to find the 10th term means n= 10)

$S_{10}$ =

(follow the formula, and use the caluator to caluate the 10th power)

Week 1- My Arithmetic Sequence

Posted on February 4, 2018 by hanluq2015

1: my own arithmetic sequence: 20，22，24，26，28，30

first five numbers: 20, 22, 24, 26, 28,30

2: $t_{1}+49d=t_{50}$ , d=2

20+49×2=t_{50}=118

3: $latex t_{1}+(n-1)d=t_{n}

=20+(n-1)2

=20+2n-2

=18+2n

4:(sorry Ms Burton, I don’t know how to type the formula, but I post the process oƒ calculating the sum of the 50 terms)

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