Final answer:
The equation of the parabola with vertex at (0,2) and passing through the point (-20,-18) is y = -1/20(x²) + 2.
Step-by-step explanation:
The student is asking for the equation of a parabola in vertex form that opens up or down, has a vertex at (0,2), and passes through the point (-20,-18). The vertex form of a parabola is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola. Here, h = 0 and k = 2, so the equation simplifies to y = a(x²) + 2.
We can find the coefficient 'a' by plugging in the coordinates of the given point (-20, -18) into the equation. So we get:
-18 = a(-20²) + 2
From this equation we can solve for 'a':
-18 = 400a + 2
-20 = 400a
a = -20 / 400
a = -1/20
Therefore, the equation of the parabola in vertex form is y = -1/20(x²) + 2.