I have a test tomorrow at 10 am.. it's 9:30 right now. I really need help with understanding implied domain. my teacher never fully explained it, and now i'm panicing. He would like us to put it in interval notation, with teh sideways 8 looking things. PLEASE HELP!
also, how to put a quadratic function into vertex form...
i.e. f(x)= x^2+5x+6 and g(x)= x^2+3
Thank you!
well, this is an example and i'm totally confused as to wear my teacher got a 2... you'll understand when you see this:
Finding the vertex by completing the square
h(x)=x^2+9x+20
=x^2+9x+(9/2)^2-(9/2)^2+20
=(x+9/2)^2-81/4+20
=(x+9/2)^2-81/4+80/4
=(x+9/2)^2-1/4
and it says the vertex is (-9/2, -1/4)
..i don't understand where the two that divides the 9 comes from. i'm totally lost!
it is a property of perfect squares that the lone constant is always the square of 1/2 the coefficient of x. since the coefficient of x is 9, to have a complete square, we need the constant to be (9/2)^2. since it was not there, we add it, but since we added something that was not there, we subtract it again right after. then we can transform the first three terms into a complete sqaure, and simplify the left overs to get what you see
also, is there anyway you can help me with three more things..
the inverse of--
f(x)=(x+2)/(x+9) and f(x)=(5)/(11x-6)
evaluating functions..
k(x)=3x^2-7 for k(2x^5)
my answer was 6x^7-7, but the answer is 12x^10-7
and finding the slope-intercept form when being given a point and the slope.
for example.. m=-3 with the point (-1,2)
PS. i really appreciate all of your help!
say for the first.
f(x) = (x + 2)/(x + 9)
Let y = f(x)
so we have
y = (x + 2)/(x + 9)
for the inverse, switch x and y and solve for y. that will give you the inverse function
that is, solve x = (y + 2)/(y + 9) for y
the other is done in the same way
k(2x^5) means, you replace all the x's in k(x) with 2x^5evaluating functions..
k(x)=3x^2-7 for k(2x^5)
my answer was 6x^7-7, but the answer is 12x^10-7
so, k(2x^5) = 3(2x^5)^2 - 7
now simplify, bearing in mind the laws of exponents
start with the point-slope form:and finding the slope-intercept form when being given a point and the slope.
for example.. m=-3 with the point (-1,2)
the point slope form is: . where is the slope, and is a point the line passes through. if we expand the right hand side of this and solve for y, we get the slope intercept form: y = mx + b
so, you want to solve for y