Answer:
Vertex: (-3, 0); Opening: Upward; Axis of Symmetry: x = -3
Step-by-step explanation:
- Since the given equation is in the Vertex Form y = (x - h)²+ k, where (h, k) is the Vertex. we can find the Vertex by simply identifying h and k.
y = (x + 3)²; where h is -3 and k is 0; Therefore the vertex is at (-3, 0)
- To find the opening of the parabola, just identify whether the quadratic term is positive or negative. If positive, the opening is upward while If negative, the opening is downward.
y = (x + 3)²; if we simplify the equation we will get: y = x² + 6x + 9 and we will see that the quadratic term is positive. Therefore, the opening of the parabola is upward.
- To find the axis of symmetry use the formula: x = -B/2A. where A is the coefficient of the quadratic term and B is the coefficient of the linear term. Solution:
x = -B/2A ⇒ x = -(6)/2(1) ⇒ x = -6/2 ⇒ x = -3; Therefore, the axis of symmetry is x = -3.
