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and what do we need to do with this?
state the direction and the # of in which the graph of each function is translatedfrom the graph of f(x) = x squared
x^2 normally rests on the x-axis, but this one is moved up by 8 units
since the 1st cooeficient is positive, it open up
would it be wide or narrow
If we let g(x) = \(x^2\) and f(x) = \(x^2+8\). We can see that f(x) will always be 8 units higher on the y axis than g(x) is. Thus f(x) is a translation of the graph of \(x^2\) up 8 units.
it is neither wider nor narrower than x^2, since there is no number other than a 1 infront of the x^2 part.
so it would stay same ok thanx
larger than one tends to make the slope steeper... and narrows the graph a fraction of a slope tends to flatten the slope and widen the graph
what if there is no y intercept like f(x) = 2x squared
the y intercept is there...its just zero :)
oh ok sorry im just startin alegebra 2 x.x a little rusty
y intercept just means tha the line of the graph gets intercepted, cuahgt by, crosses over, the y axis at a certain point. another name for the y axis is x=0. so whenever x=o you can find the y intercept
y = 2(0)^2...the y int = 0
y = (0)^2 + 8 the y int = 8
so if x=o there is no direction?
you have to define what you mean by "direction"
like on the first problem u found out the the graph is going 8 units
y = (x + "moves it side to side")^2 + "moves it up or down"
you understand that little "equation" I made?
i think so like if it were to be f(x)=2x sqaured the y will be a zero? so that will mean it has no direction?
correct as far as I am understaning your choice for "direction".. it simply means that the graph itself hasnt moved anywhere....but that "2" there means that the graph did get steeper...narrower
ok thank u :D
ok one more question how would u graph all of this usin y=mx+b or no
id go with no,.... y = mx +b makes a line...not a curve y = Mx^2 + b makes a curve since it has a "2" on the x. starts to bend the line