Mathematics
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OpenStudy (anonymous):
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jimthompson5910 (jim_thompson5910):
for #2, going from y = x^2 to y = k*x^2 stretches the graph vertically by a factor of k
if k is negative, then you'll flip the graph over the x axis
jimthompson5910 (jim_thompson5910):
k can be any constant
jimthompson5910 (jim_thompson5910):
I'm just stating the general rule
jimthompson5910 (jim_thompson5910):
for example, say we go from y = x^2 to y = 3x^2
k in this case is k = 3
jimthompson5910 (jim_thompson5910):
so y = x^2 is being stretched vertically by a factor of 3
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jimthompson5910 (jim_thompson5910):
going from y = x^2 to y = (x-h)^2 shifts the graph h units to the right
if h is negative, then you're shifting |h| units to the left
jimthompson5910 (jim_thompson5910):
y=(-3x)^2 is the same as y=9x^2 after you square each piece
jimthompson5910 (jim_thompson5910):
correct
jimthompson5910 (jim_thompson5910):
since h = 5
jimthompson5910 (jim_thompson5910):
y=(-3x)^2 is the same as y=9x^2 after you square each piece
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jimthompson5910 (jim_thompson5910):
so #2 and #4 use the same basic rule
jimthompson5910 (jim_thompson5910):
by a factor of _______
jimthompson5910 (jim_thompson5910):
fill in the blank
jimthompson5910 (jim_thompson5910):
9 actually since we're dealing with y = 9x^2
jimthompson5910 (jim_thompson5910):
y=(-3x)^2 is equivalent to y=9x^2
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jimthompson5910 (jim_thompson5910):
yes
jimthompson5910 (jim_thompson5910):
what do you have so far
jimthompson5910 (jim_thompson5910):
x intercepts are of the form (x,0)
jimthompson5910 (jim_thompson5910):
the vertex is an ordered pair
not a single point
jimthompson5910 (jim_thompson5910):
you have your coordinates mixed up
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jimthompson5910 (jim_thompson5910):
(x,y) not (y,x)
jimthompson5910 (jim_thompson5910):
vertex is really (-1,-3)
jimthompson5910 (jim_thompson5910):
correct
jimthompson5910 (jim_thompson5910):
x-intercepts are the points where the graph crosses the x axis
jimthompson5910 (jim_thompson5910):
the y-intercept is the point where the graph crosses the y axis
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jimthompson5910 (jim_thompson5910):
x intercepts are of the form (x,0)
always
jimthompson5910 (jim_thompson5910):
so if the graph crosses the x axis at 7, then (7,0) is one x-intercept
jimthompson5910 (jim_thompson5910):
"axis of symmetry is -1?" correct
jimthompson5910 (jim_thompson5910):
intercepts are (-3,0) and (1,0)
jimthompson5910 (jim_thompson5910):
you made a typo on your second root
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jimthompson5910 (jim_thompson5910):
what is the y-intercept?
jimthompson5910 (jim_thompson5910):
where does it cross the y axis?
jimthompson5910 (jim_thompson5910):
look closer
jimthompson5910 (jim_thompson5910):
the curve cutting across the vertical y axis
jimthompson5910 (jim_thompson5910):
nope but close
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jimthompson5910 (jim_thompson5910):
yep -3 so the y intercept is (0,-3)
jimthompson5910 (jim_thompson5910):
specifically
x-intercepts: (-3,0) and (1,0)
y-intercept: (0,-3)
jimthompson5910 (jim_thompson5910):
I would point out which intercepts are what (are they x-intercepts? or y-intercepts?)
jimthompson5910 (jim_thompson5910):
what do you mean?
jimthompson5910 (jim_thompson5910):
I'm not sure either
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jimthompson5910 (jim_thompson5910):
I'm not that great at physics
jimthompson5910 (jim_thompson5910):
when x = 0, what is y?
jimthompson5910 (jim_thompson5910):
y=x^2-2x-3
y=(0)^2-2(0)-3 ... replace every x with 0
y = ???