how to know if a parabola is vertical or horizontal?

Question

How can I tell if a parabola is vertical or horizontal given the vertex at (0,-2) and a point at (3,4)? Thank you!

Answer 1

y = ax² + bx + c is the general form of a parabola.



Using point (0, -2) we get:



-2 = c



so, y = ax² + bx - 2



At the vertex, dy/dx = 0



so, dy/dx = 2ax + b = 0



i.e. b = 0



Then y = ax² - 2



Using point (3, 4) we get:



4 = a(3²) - 2



=> a = 6/9 = 2/3



so, y = 2x²/3 - 2....i.e. vertical



Here is a sketch:



http://www.wolframalpha.com/input/?i=y+%3D+2x%C2%B2%2F3+-+2



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Answer 2

A vertical parabola is of the form y=x^2. A horizontal is of the form x=y^2

Answer 3

We simply did this in these days. Adequate, the commonplace parabola form is x²=4py, with p equalling both the asmptote and the focus. The course is recognized by means of whether or not x² or y² is first; if it is x²=4py, the parabola is vertical. If it is y²=4px, it can be horizontal. Whether or not it goes up, down left or proper will depend on if p is positive or terrible; positive makes it go up or correct (depending on whether it can be hori or vert) and bad makes it down or left. So, for those who had x²=12y, your focus would be (zero, four) and your asymptote can be x=-four. It might be vertical and opening up.. The vertex is regularly the beginning (zero,zero); if no longer, it follows the form (y-y1)²=4p(x-x1). Nevertheless, converting your equation to commonplace has to do with utilizing vertex type, which we've not learned yet. I am hoping what I gave you so far helps though.

Answer 4

y=k(x-0)^2-2



since it goes through the point (3,4)

4=k(3)^2 -2

k=6/9=2/3



The equation of parabola is y=(2/3)x^2-2





it is vertical

Answer 5

you need more information, two points form a line and could possible form either a vertical or a horizontal parabola



A related equation

Boundary conditions

You need something else

Answer 6

put in the equation of horizontal and vertical parabola ... if it satisfies ,it would be that one ..

Answer 7

With the information given,it can be either. Just one more point needed.

Answer 8

Generally according to vertical if there is solution.