Question

What is the equation of the parabola whose vertex lies on the coordinates (12, 7)?

Answer 1

I'm going to solve this in vertex form.

The equation for vertex form is \[y = a(x - h)^{2} + k\], where h is the x coordinate and k is the y coordinate (h, k)

Now, we need to plug that in, and if we do that, we'll get:

\[y = a(x-12)^{2} + 7\]

The point of "a" in the beginning of the equation is to tell us whether the parabola opens up or down. So:

If a> 0, the parabola opens upwards
if a< 0, it opens downwards.

Finally, if you need to find the axis of symmetry (basically the line where the vertex lies) the equation is: \[-b \div 2a\].

Any more info: http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php

Answer 2

You can also put the coordinates into standard form, which is \[y = ax ^{2} + bx + c\].

Answer 3

A bit of an excessive reply, but does that answer your question?

Answer 4

also, this goes in the math section. not computer science.