Question

A quadratic function goes through the points (−3, 3), (−1, 3), and (−2, 4). What is the axis of symmetry? Its vertex? Its equation?

Answer 1

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.