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

Apr 19, 2015

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

$y - \left(- 5\right) = a \left(x - \left(- 2\right)\right) \Rightarrow y + 5 = a {\left(x + 2\right)}^{2}$

where $a$ is the amplitide.

E.G.:

$a = 1 \Rightarrow y + 5 = {\left(x + 2\right)}^{2}$
graph{y+5=(x+2)^2 [-10, 10, -5, 5]}

$a = 3 \Rightarrow y + 5 = 3 {\left(x + 2\right)}^{2}$
graph{y+5=3(x+2)^2 [-10, 10, -5, 5]}

$a = \frac{1}{2} \Rightarrow y + 5 = \frac{1}{2} {\left(x + 2\right)}^{2}$
graph{y+5=1/2(x+2)^2 [-10, 10, -5, 5]}

$a = - 2 \Rightarrow y + 5 = - 2 {\left(x + 2\right)}^{2}$
graph{y+5=-2(x+2)^2 [-10, 10, -15, 15]}