Question

Write the equation of the parabola in vertex form.
vertex (3,3), point (2, - 1)

Answer 1

Explanation:

The vertex form of a parabola is given by

`y = a(x - h)^2 + k`

where (h, k) are the coordinates of the vertex of the parabola. So we can write our parabola as

`y = a(x - 3)^2 + 3`

We know that our curve goes through the point (2, -1) so we can solve for the constant a as follows:

`-1 = a(2 - 3)^2 + 3 \Rightarrow -1 = a + 3`

or

`a = -4`

Therefore, the vertex form of the equation for the parabola is

`y = -4(x - 3)^2 + 3`