parabola (vertical--> up and down)

y- k = a (x-h)^2 vertex (h,k) graph by walking 2c from the focus a = 1/4c

(x - h)^2/a^2 + (y-k)^2 /b^2= 1

(x - h)^2/b^2 +(y-k)^2 /a^2= 1 -the bigger number (a or b) is under the major foci: the square root of a^2 - b^2 a^2-b^2 = c^2

hyperbolas (horizontal)

-a does not have to be > b (x-h)^2/a^2 - (y-k)^2/b^2 = 1 transverse axis: the one that's positive asymptotes (the diagonal lines): y=±b/a(x−h)+ k foci: square root of a^2 + b^2 a^2 + b^2 = c^2

hyperbolas (vertical)

(y-k)^2/a^2 - (x-h)^2/b^2 = 1 asymptotes: y−k=±a/b(x−h) +k

identify without graphing: circle

x^2 and y^2 have the same coefficient -alawys positive (every term must be positive --> if you have to divde then every term should be positive after division

identify without graphing: elipse

different coeficcents of x^2 and y^2 -both have the same sign (- or +)

identify without graphing: hyperbola

x^2 and y^2 have opp. signs -both have opposite signs

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Math

Question	Answer
parabola (vertical--> up and down)	y- k = a (x-h)^2 vertex (h,k) graph by walking 2c from the focus a = 1/4c
parabola (horizontal --> left and right)	x - h = a (y-k)^2
for parabola word problems , what is the formula for x	x = -b/2a
ellipse horizontal	(x - h)^2/a^2 + (y-k)^2 /b^2= 1
vertical elipse	(x - h)^2/b^2 +(y-k)^2 /a^2= 1 -the bigger number (a or b) is under the major foci: the square root of a^2 - b^2 a^2-b^2 = c^2
circle equation	(x - h)^2 + (y+2)^2 = r^2
hyperbolas (horizontal)	-a does not have to be > b (x-h)^2/a^2 - (y-k)^2/b^2 = 1 transverse axis: the one that's positive asymptotes (the diagonal lines): y=±b/a(x−h)+ k foci: square root of a^2 + b^2 a^2 + b^2 = c^2
hyperbolas (vertical)	(y-k)^2/a^2 - (x-h)^2/b^2 = 1 asymptotes: y−k=±a/b(x−h) +k
identify without graphing: circle	x^2 and y^2 have the same coefficient -alawys positive (every term must be positive --> if you have to divde then every term should be positive after division
identify without graphing: elipse	different coeficcents of x^2 and y^2 -both have the same sign (- or +)
identify without graphing: hyperbola	x^2 and y^2 have opp. signs -both have opposite signs
identify without graphing: parabola	only one squared term
identify without graphing: lines	no squared terms

Created by: Blessed Rectangle 10

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