This week in math, we did review of everything before spring break, and started learning about how to graph quadratic formulas. 

Depending on the given function, we can determine many things, such as opening, vertex, domain and range.

For example:

f(x) = -2(x + 4)^2 – 1

Because this number is a negative, the parabola opening will be downwards.

The number with the x in brackets is always the x-intercept, but opposite symbol. So this one, would be -4. The number after brackets will always be the y-intercept, not opposite. So this one, would be -1.

V = (-4, -1)

The domain is always XER

Range = y < -1

My biggest mistake this week was always forgetting to switch the symbol of the x-intercept, which always lead me to having the wrong function.

This week in math, we combined our knowledge of perfect squares and trinomials into something called perfect square trinomials! These are special because they don’t factor.

Perfect squares are numbers where an integer has multiplied itself, resulting in a product which can be defined as a perfect square, and a trinomial is an expression with three terms. Perfect Square Trinomials are Trinomials where it does not factor, meaning a different method needs to be used. x^2 +8x + 5, for example, can only be defined by 5 x 1, and when you add 5 and 1, it does not equal 8, meaning it is not a trinomial which can factor.

My biggest mistake this week was just something difficult for me to do:

To factor a trinomial such as x^2 + 8x + 5 = 0 the first step is moving the third term in the trinomial over to the right side of the equation, which will be “c”.

x^2 + 8x + 0 = -5.

The second step is dividing the second term (8), by two (8/2 = 4), then squaring it, (4^2 = 16)

x^2 + 8x +16 = 11

From here, we can factor the trinomial x^2 + 8x + 16

(x + 4)^2.

Now we can square root both sides,  √(x + 4)^2 = √11

This would give us the final answer of  x = -4+/-√11

This week in math, we reviewed the concept of factoring a binomial with a difference of squares, which was a much needed review for me since I took math in first semester last year.

A difference of squares is used to refer to a binomial like 4x^2 – 16, where both 4 and 16 are perfect squares and have a subtract symbol in the middle, to show a difference. For expressions with a difference of squares, something I needed to review was that we can just square root each number and put it into brackets with opposite symbols in both brackets to symbolize the negative…

√4 = 2     √16 = 4

(3x + 4)(3x – 4)

My biggest mistake this week was, that I kept on forgetting how to factor with a coefficient in front of the x^2. I kept thinking I could just take it out and keep the rest of the equation in brackets, but that always ended up confusing me. To get it right I have to…

9x^2 + 6x + 1

multiply these two —-> 9x^2

what two numbers multiplied can equal to 9 when multiplied and 6 when added?

3 x 3

(9x^2 + 3x)(3x + 1)

divide what is in the brackets by common factors! then leave that out of the brackets.

3x(3x +1)1(3x + 1) the two brackets should equal the same thing!

(3x + 1)(3x + 1) 0r… (3x + 1)^2

This week in math we learnt a bit more on multiplying and dividing radicals, and how to rationalize the denominator in a radical division or fraction. I was relieved and happy this week, because this area of focus seems to make sense to me.

When you have a radical in the denominator of a fraction, you want to try make it into… NOT a radical! To do this, you have to multiply the top and bottom by the radical inside the denominator, then make a 0 pair, evaluate the top and bottom, and get your most simplified answer! When multiplying the numerator and denominator by the denominator’s radical, you must switch any addition symbols to a subtraction, and vice versa. For example:

     2√3         ×   3√2 − √3    →       6√6 − 2√9          →          6√6 − 6      =   2√6 − 2

3√2 + √3    ×   3√2 − √3         9√4 − 3√6 + 3√6 − √9                   15                      5

                                            18              −             3

The biggest mistake I made was not knowing that  if the signs are opposites on the top and bottom (√3 + 4 over √5 − 2), the signs have to be opposites of both, not just the denominator (× √3 − 4, × √5 + 2).

This week in math, we focused a lot on adding and subtracting radicals. This one was a bit trickier than normal for me, but me table group helped a lot.

At first I thought an equation like  4√3 + 6√3 would equal to 10√6, but that was my mistake this week, which I thankfully learnt about, thanks to my table group.

To make the proper equation, you would go through the steps of adding together the coefficients, but leaving the radicand if it is the same! You leave it as the same number because it is being multiplied by the coefficients. So correctly, this would equal to…

4√3 + 6√3 = (4+6) = 10√3!

This week in pre-calculus, we reviewed exponent laws, and learnt a new law for fractional exponents! Reviewing the laws went pretty smoothly for me, as that’s one of the things that I always understood, and learning the new law was a bit confusing at first, but then I realized how simple it was, thanks to Ms. Burton.

The new exponent law is that when you have a number with a fractional exponent, the denominator always goes into the index of a root! So, if I were to have 4^5/3, written out as a root, it would be  (3√72)5.

This was the rule I had a hard time remembering, which resulted in quite a few mistakes, until Ms. Burton taught us the saying “FLOWER POWER”! This helps because the root of the flower is first – so the denominator because it’s on the bottom! (Thanks Ms. Burton)

This week in class, we did a lot of review on grade 10 subjects, which, to be honest, I had forgotten a lot of. We reviewed on different types of numbers and got straight into learning about square and cube roots! A square root is when a number can be cut down into the same number times itself.

For example, the square root of 36 is 6, because 6x 6 is 36! A cube root has a very similar concept, except a number times itself 3 times – so the cube root of 8 is 2, because 2 x 2 x 2 is 8!

A big mistake I kept making but eventually strayed away from was adding a number two times, instead of multiplying it (2 + 2, 2 x 2) – it didn’t happen as much with the cube roots so much as the square roots. But I quickly would realize my mistake every time.