Answer:
y - 4 = (-3/2)(x + 3)^2
Step-by-step explanation:
The vertex of the given graph is at (-3, 4), and the graph also goes through (-1, -2). Using the vertex equation of a parabola, y - k = a(x - h)^2, and inserting the given info: vertex at (-3, 4) => h = -3, k = 4; other point at (-1, -2) => x = -1, y = -2.
Then:
y - k = a(x - h)^2 becomes -2 - 4 = a(-1 + 3)^2, or:
-6 = 4a. Therefore, a = -6/4, or a = -3/2. The equation of this quadratic is:
y - 4 = (-3/2)(x + 3)^2
