Final answer:
The equation of the parabola with a vertex at (-3,4) and passing through (10, -89/20) is y = (-1/20)(x + 3)^2 + 4.
Step-by-step explanation:
The parabola with a vertex at (-3,4) and passing through the point (10, -89/20) can be written in the vertex form of a quadratic equation,
which is y = a(x - h)^2 + k,
where (h,k) is the vertex of the parabola.
To find the value of 'a', we use the point (10, -89/20) that lies on the parabola.
Substituting the point into the vertex form, we get -89/20 = a(10 - (-3))^2 + 4.
Solving for 'a' gives us a = (-89/20 - 4) / (10+3)^2.
Simplifying this, we get a = (-89/20 - 80/20) / 169,
which further simplifies to a = -169/20 / 169, resulting in a = -1/20.
Thus, the equation of the parabola is y = (-1/20)(x + 3)^2 + 4, which is in vertex form.