Question

If we know the vertex of a parabola is (-2,-5), can we figure out the equation of the parabola?

Answer 1

No, because three data are necessary. If the vertex is known you can write:

`y-(-5)=a(x-(-2))rArry+5=a(x+2)^2`

where `a` is the amplitide.

E.G.:

`a=1rArry+5=(x+2)^2`
graph{y+5=(x+2)^2 [-10, 10, -5, 5]}

`a=3rArry+5=3(x+2)^2`
graph{y+5=3(x+2)^2 [-10, 10, -5, 5]}

`a=1/2rArry+5=1/2(x+2)^2`
graph{y+5=1/2(x+2)^2 [-10, 10, -5, 5]}

`a=-2rArry+5=-2(x+2)^2`
graph{y+5=-2(x+2)^2 [-10, 10, -15, 15]}