Answer:
y = -3(x + 1)^2 + 2
Explanation:
y = a(x - h)^2 + k is the vertex form of a quadratic, where
- (x, y) are any point that lies on the parabola,
- a is a constant determining whether the parabola opens upward or downward,
- and (h, k) are the coordinates of the vertex.
Finding (h, k):
We see from the graph that the vertex is a maximum and its coordinates are (-1, 2). Thus h is -1 and k is 2. Since h becomes negative, it will be 1 in the parentheses: (x - (-1) = (x + 1).
Finding a:
In order to find a, we will need to plug in a point on the parabola for (x, y) and (-1, 2) for h and k. We see that (0, -1) lies on the parabola so we can use this point for (x, y).
-1 = a(0 - (-1))^2 + 2
-1 = a(0 + 1)^2 + 2
-3 = a(1)^2
-3 = a
Thus, a = -3.
Thus, the exact equation in vertex form of the parabola is:
y = -3(x + 1)^2 + 2
I attached a picture from Desmos Graphing Calculator that shows how the equation I provided works and contains the two points you marked on the parabola, including (-1, 2) aka the maximum, and (0, -1) aka the y-intercept.