Methods - Transformation of graphs

Parabola, hyperbola, y²=x, y=√x, Circle, Semicircles

Parabola

y=a(x-h)² +k

Para algebra meaning

h-left/right (opposite to sign i.e. - goes right, + goes left)
k-up/down (same as sign)
negative ‘a’ means reflection

hyperbolas

y=a/(x-h)+k

hyperbolas algebra meaning

-a scales the graph to expand/compress
-h translates the graph left/right (opposite to sign)
-k translates the graph up/down (same to sign)
-The asymptote are x=h and y=k
-if negative sign is present before the faction, reflect graph

y²=x

(y-k)²=a²(x-h)

y²=x algebra meaning

Vertex - (h,k)

Axis of symmetry - y=k

k-up/down (opposite to sign)

h-left/right (opposite to sign)

y=√x

y = a√(x − h) + k

y=√x algebra

if x is negative reflect

h-left/right (opposite to sign)

k-up/down (same as sign)

endpoint - (h,k)

Circle

(x-h)²+(y-k)²=r²

Circle algebra meaning

(h, k) - centre of the circle
r - the radius of the circle
k-up/down (opposite of sign)
h-left/right (opposite of sign)