help!! (1 Viewer)

[iheartgeorge]

can anybody explain how to do this one:
find the equation of a curve that is always concave upwards with a stationary point at (-1,2) and y intercept 3

 

[pLuvia]

Since the graph is always concave upwards, hence it is a parabola. And a parabola only has one stationary point which is the vertex. And using the general equation of a parabola
x²=4ay
(x+1)²=4a(y-2)
x²+2x+1=4ay-8a
x²+2x+(1+8a)=4ay
[x²+2x+(1+8a)]/4a=y

Y intercept is 3
(1+8a)/4a=3
1+8a=12a
4a=1
a=1/4

.: The equation of the parabola is (x+1)²=(y-2)

 

[Slidey]

What about y=x^(2n), n natural?



It's lucky the question says "find the equation of a curve".