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Mathematics 29 Online
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

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

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

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

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

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

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

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

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 = ???

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