Answer: y = -1/3(x + 1)² + 4
Explanation:
First of all, we know that the graph is going to be a parabola
So we can start off with the parent function, y = x²
Using vertex form, y = a(x - h)² + k, where the vertex is point (h, k):
we have the formula: y = a(x + 1)² + 4
If the parabola must pass through the point (2,1), we can substitute these for x and y in our equation to find a, and finish the problem:
1 = a(2 + 1)² + 4
-3 = a(3)²
-3 = 9a
a = -1/3
based on this, our final formula will be y = -1/3(x + 1)² + 4