# Thread: I need and explaination

1. ## I need and explaination

I have not taken a math class for two years and need a little refreshing.

Find the standar equation of a parabola that has a vertical axis and satisfies the given conditions.

Vertex (3,5) x-intercept 0

I need help solving this and an explaination on how to solve equations like this in general. Thanks!!

2. Originally Posted by niniu_blue
I have not taken a math class for two years and need a little refreshing.

Find the standar equation of a parabola that has a vertical axis and satisfies the given conditions.

Vertex (3,5) x-intercept 0

I need help solving this and an explaination on how to solve equations like this in general. Thanks!!
Something wrong with the Question. x-intercept is what? It is 0 only? That is incomplete.

However, if that is all that is given, and the Question is complete or is posted correctly, then "x-intercept 0" may mean the origin (0,0) is an x-intercept.

The standard form of the squation of a "vertical" parabola--or a parabola whose axis of symmetry is vertical--is
(y-k) = a(x-h)^2 ------------(i)
where
(h,k) is the vertex.
"a" is any real number.

So if the vertex is at point (3,5), the Eq.(i) becomes
(y -5) = a(x -3)^2 ---------(ii)

What is "a"?
At the x-intercept (0,0), Eq.(ii) becomes
(0 -5) = a(0 -3)^2
-5 = 9a
a = -5/9 --------------***

Therefore, the parabola is
y -5 = (-5/9)(x -3)^2 ---------------answer.