Category: Math 11

 

at first adding and subtracting is all very simple and it all comes around to one common thing among all addition questions, the common denominator.

no question with a different denominator does not work with addition or subtraction, they must have the same.

For our question our common denominator was 15x

so we multiplied the first side by 5 making it 20/15x and the second side by 3 making it 3/15x

adding these is just one step now because of the common denominator

it is 23/15x

How to find a parabola on  graph.

these equations are all examples of a parabola:

y=2x^2

y=(x-3)^2+4

y=3(x+2)^2-2

were going to use this last one as an example, it all starts with the parent function: y=x^2, heres what it looks like

if it has a number out front of the x or bracket, that is the “slope” of the line, and multiplies the parent function by whatever number is out front.

it will only move side to side, if there are brackets around the x and a number, if the number is negative, it will move to the right, if it is positive, the whole parabola will move to the left.

the last number is the y intercept, it is the same as graphing slope lines, it moves the parabola up and down.

for our equation y=3(x+2)^2-2, the slope would be 3, it would move over 2 to the left, and down 2

Completing the squares is a bit complicated, it involves adding a “zero pair” which is adding and subtracting the same number. This is to make the rest of the equation line up. This works best if factoring is not a possibility.

example:

+ 6x+2=0

this wouldn’t be able to factor, there are no 2 positive numbers that add into 6 and multiply into 2.

this is where we make our zero pair

+ 6x+9-9+2=0

we add this so we can square the first 3 numbers

-7 = 0

= 7

now we can square root everything

X + 3 =  + –

X = -3 +-

Working with exponents gets pretty easy once you get the hang of it, fraction exponents are a little bit more complicated.

say you have   , you’re going to want to put it into a root, the denominator will always be the root.

a tip for this is flower power, by showing that the roots are always on the bottom

so this would look like

the numerator always becomes the exponent on whatever is in the root

in our case it is cubed root of 8 to the power of 2

to simplify this, we can do the cubed root of 8, equaling 2, and 2 to the power of 2 is 4

the answer for this question would be 4

working with the same equation but the exponent is negative, it would be the same answer, just reciprocated and put under a one

an entire radical, is a whole square root and looks like this:

a mixed radical, has a visible coefficient, and will look like this

say we have

we have to first look into some numbers that multiply into 25

1*125

5*25

now we have to look for any square roots within these numbers

25 is a perfect square

therefore = = 5