Given the vertex and a point on the parabola, write an equation in vertex form

Vertex: (-6,-2) ; Point: (-3,4)

1 answer

The vertex form of a parabola with vertex (h, k) is given by the equation y = a(x - h)^2 + k.

Using the given vertex (-6, -2), we substitute these values into the equation:

y = a(x - (-6))^2 + (-2)

Simplifying:

y = a(x + 6)^2 - 2

Now, we need to find the value of "a" by substituting the coordinates of the given point (-3, 4):

4 = a((-3) + 6)^2 - 2

Simplifying further:

4 = a(3)^2 - 2
4 = 9a - 2
9a = 6
a = 6/9
a = 2/3

Substituting the value of "a" back into the equation, we have:

y = (2/3)(x + 6)^2 - 2

Therefore, the equation in vertex form is y = (2/3)(x + 6)^2 - 2.