Answer:
Vertex at (-2, 4); axis of symmetry is x = -2; y = a(x + 2)² + 4
Step-by-step explanation:
y = ax² + bx + c
1. Vertex
The points that satisfy the equation are (−3, 3), (−1, 3), and (−2, 4).
Fig. 1 shows the three points. The parabola opens down, with a vertex at (-2, 4)
2. Axis of symmetry
The axis of symmetry is x = -2, as in Fig. 2
3. Equation
The vertex form of a parabola is
y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
If the vertex is at (-2, 4), the equation is
y = a(x + 2)² + 4
Insert the point (-1, 3)
3 = a(-1 +2)² + 4
3 = a(1)² + 4
3 = a + 4
a = -1
The equation in vertex form is
y = -(x + 2)² + 4
Fig. 3 shows the inverted parabola passing through the three points.