I BEG you to help me with my algebra 2 review...?

Question

and dumb it down as much as possible too please.

i won't ask for the actual answers but how to do the stuff instead.

i need to know how to graph an equation like y=(x+1)^2-3 and i need to know how to find the domain and range of an equation like that

also i need to know HOW to do an equation like this f(x)=1/x; g(x)=x^2-4

what are square root properties and what is meant by completing the square?

i swear if you help me,i'd love you forever and ever!

Answer 1

Graphing tricks!: Get a basic feel for the graph.  Try to recognize shifts of basic equations.  Like, (x+1)^2 - 3 is just x^2 but shifted to the right one unit and down three units!  (Dont be worried if you have no clue what im talking about, you'll get it after a little practice.)

Find all the intercepts and asymptotes of the equation and put points/lines where they are.  Next plug in numbers for x which make for simple arithmetic of the function.  E.g.  for y=(x+1)^2-3, just plug in x=-1 and you get y=-3.  Plug in numbers around 1 and the intercepts to get the general idea of the function.

In order to find the domain and range of an equation you have to think about what can x be in the equation.  So for y=(x+1)^2-3, x can be anything!  For the range you have to figure out what y can be, but this is a little trickier...unless you rearrange the equation.

    y+3=(x+1)^2

    sqrt(y + 3)=x + 1

Now when you have y under the sqrt sign, immediately think about what y has to be in order to make everything under the sqrt sign negative.  What if y is -3, then sqrt(y + 3) is 0, but if y is less than -3... then you get an imaginary number.  So y has to be greater than -3, and that is the range.

For the equation f(x)=1/x, just be cautious about asymptotes and what the graph approaches near them.

As for square root properties, if you are taking the square root of a constant, e.g. 9 the answer is always positive. However, if you have an equation like x^2=9, then you must think about what number squared can =9, 3 OR -3.

Completing the square is just another method of factoring.  Say you have an equation y= x^2 + 4x + 5, you complete the square by finding the constant that is half of the middle term squared.  Half of 4 squared is 4, therefore we want x^2 + 4x + 4, because this factors to (x + 2)^2!   Wait though, we still have a 1 left over, so we complete the expression by writing (x + 2)^2 + 1= y.  Multiplying that back out we get the more complicated form x^2 + 4x +5, but it's all the same.

Answer 2

u can google: range, domain, square root properties, completing the square.

they will give u examples and good explanations.

on plotting equations, the best way is to make an x and y table, get the y value for each x.