Question

Find the equation of a parabola with a vertical axis and its vertex at the origin and passing through the point (-2, 3).

Answer 1

`y=(3)/(4)x^2`

Explanation:

Hi there!

Because we're given the vertex of the parabola, we can determine its equation in vertex form:

`y=a(x-h)^2+k` where the vertex is
`(h,k)`

Plug in the vertex (0,0)

`y=a(x-0)^2+0\\y=a(x)^2\\y=a(x-0)^2+0\\y=ax^2`

Now, we must solve for a. Plug in the given point (-2,3) and solve for a:

`3=a(-2)^2\\3=4a\\(3)/(4) =a`

Therefore, the value of a is
`(3)/(4)`. Plug this back into
`y=ax^2`:

`y=(3)/(4)x^2`

I hope this helps!