The general equation of a parabola in vertex form is y = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex.
We are given that the vertex is (6, -6). So, h = 6 and k = -6.
We also know that the parabola passes through the point (8, -14). Plugging in these values into the equation, we get:
-14 = a(8-6)^2 + (-6)
Simplifying the equation further:
-14 = a(2)^2 - 6
-14 = 4a - 6
Rearranging the equation to solve for a:
4a = -14 + 6
4a = -8
a = -8/4
a = -2
Now that we have the value of a, we can write the equation of the parabola in vertex form:
y = -2(x-6)^2 - 6
Therefore, the equation of the parabola in vertex form is y = -2(x-6)^2 - 6.
Question Suppose a parabola has a vertex (6, -6) and also passes through the point (8, -14). Write the equation of the parabola in vertex form.(1 point) show all your work
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