Graphing A Parabola From Vertex Form Worksheet - Fill and Sign ... - Free Printable

I'll solve this worksheet on graphing parabolas from vertex form. Let me go through each problem step by step.

First, let me recall that the vertex form of a parabola is: y = a(x - h)² + k
where (h, k) is the vertex of the parabola.
- If a > 0, the parabola opens upward and the vertex is a minimum.
- If a < 0, the parabola opens downward and the vertex is a maximum.
- The axis of symmetry (A.O.S.) is the vertical line x = h.

Now, let's solve each problem:

Problem 1: y = (x - 4)² + 2
- Vertex: (4, 2) [from (h, k) where h=4, k=2]
- A.O.S.: x = 4
- Since a = 1 (positive), the vertex is a minimum.

Problem 2: y = 2(x - 3)² + 5
- Vertex: (3, 5) [from (h, k) where h=3, k=5]
- A.O.S.: x = 3
- Since a = 2 (positive), the vertex is a minimum.

Problem 3: y = -3(x + 1)² - 4
- Vertex: (-1, -4) [from (h, k) where h=-1, k=-4; note that (x + 1) = (x - (-1))]
- A.O.S.: x = -1
- Since a = -3 (negative), the vertex is a maximum.

Problem 4: y = (x - 5)² - 3
- Vertex: (5, -3) [from (h, k) where h=5, k=-3]
- A.O.S.: x = 5
- Since a = 1 (positive), the vertex is a minimum.

Here are the completed answers for the worksheet:

1. Vertex: (4, 2)
A.O.S.: x = 4
Is the vertex a max or min? Minimum

2. Vertex: (3, 5)
A.O.S.: x = 3
Is the vertex a max or min? Minimum

3. Vertex: (-1, -4)
A.O.S.: x = -1
Is the vertex a max or min? Maximum

4. Vertex: (5, -3)
A.O.S.: x = 5
Is the vertex a max or min? Minimum