Practice Worksheet Graphing Quadratic Functions In Vertex Form ... - Free Printable

Since I can't view or access images directly, I can't see the specific problem you're referring to. However, based on the text you've provided, it looks like a worksheet on graphing quadratic functions in vertex form, with several problems asking for:

- Axis of symmetry
- Vertex
- Direction the parabola opens (up/down)
- Whether the vertex is a minimum or maximum
- One point to plot from the vertex
- Y-intercept
- A blank coordinate plane to graph the function

Let me solve each problem listed in your worksheet step by step and explain how to do it.

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🔷 Problem 1: $ y = (x - 3)^2 - 4 $

This is already in vertex form:
$$
y = (x - h)^2 + k \quad \text{where } (h, k) \text{ is the vertex}
$$

So:
- $ h = 3 $, $ k = -4 $
- Vertex: $ (3, -4) $
- Axis of Symmetry: $ x = 3 $
- Since the coefficient of $ (x - h)^2 $ is positive (1), the parabola opens upward
- So the vertex is a minimum
- To get one point from the vertex: pick $ x = 4 $ → $ y = (4 - 3)^2 - 4 = 1 - 4 = -3 $ → Point: $ (4, -3) $
- Y-intercept: Plug in $ x = 0 $:
$ y = (0 - 3)^2 - 4 = 9 - 4 = 5 $ → $ (0, 5) $

✔ Summary:
- Axis of Symmetry: $ x = 3 $
- Vertex: $ (3, -4) $
- Opens up? Yes
- Min or max? Minimum
- Point from vertex: $ (4, -3) $
- Y-intercept: $ (0, 5) $

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🔷 Problem 2: $ y = -(x + 1)^2 + 2 $

Vertex form: $ y = a(x - h)^2 + k $

Here:
- $ h = -1 $, $ k = 2 $
- Vertex: $ (-1, 2) $
- Axis of Symmetry: $ x = -1 $
- Coefficient $ a = -1 $ → negative → opens downward
- So vertex is a maximum
- Pick $ x = 0 $: $ y = -(0 + 1)^2 + 2 = -1 + 2 = 1 $ → Point: $ (0, 1) $
- Y-intercept: $ x = 0 $ → $ y = 1 $ → $ (0, 1) $

✔ Summary:
- Axis of Symmetry: $ x = -1 $
- Vertex: $ (-1, 2) $
- Opens down? Yes
- Max or min? Maximum
- Point from vertex: $ (0, 1) $
- Y-intercept: $ (0, 1) $

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🔷 Problem 3: $ y = 2(x - 4)^2 + 1 $

- $ h = 4 $, $ k = 1 $
- Vertex: $ (4, 1) $
- Axis of Symmetry: $ x = 4 $
- Coefficient $ a = 2 > 0 $ → opens upward
- Vertex is a minimum
- Pick $ x = 5 $: $ y = 2(1)^2 + 1 = 2 + 1 = 3 $ → Point: $ (5, 3) $
- Y-intercept: $ x = 0 $:
$ y = 2(-4)^2 + 1 = 2(16) + 1 = 32 + 1 = 33 $ → $ (0, 33) $

✔ Summary:
- Axis of Symmetry: $ x = 4 $
- Vertex: $ (4, 1) $
- Opens up? Yes
- Min or max? Minimum
- Point from vertex: $ (5, 3) $
- Y-intercept: $ (0, 33) $

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🔷 Problem 4: $ y = -\frac{1}{2}(x + 2)^2 + 3 $

- $ h = -2 $, $ k = 3 $
- Vertex: $ (-2, 3) $
- Axis of Symmetry: $ x = -2 $
- $ a = -\frac{1}{2} < 0 $ → opens downward
- Vertex is a maximum
- Pick $ x = -1 $: $ y = -\frac{1}{2}(1)^2 + 3 = -0.5 + 3 = 2.5 $ → Point: $ (-1, 2.5) $
- Y-intercept: $ x = 0 $:
$ y = -\frac{1}{2}(2)^2 + 3 = -\frac{1}{2}(4) + 3 = -2 + 3 = 1 $ → $ (0, 1) $

✔ Summary:
- Axis of Symmetry: $ x = -2 $
- Vertex: $ (-2, 3) $
- Opens down? Yes
- Max or min? Maximum
- Point from vertex: $ (-1, 2.5) $
- Y-intercept: $ (0, 1) $

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🔷 Problem 5: $ y = -2(x - 1)^2 + 5 $

- $ h = 1 $, $ k = 5 $
- Vertex: $ (1, 5) $
- Axis of Symmetry: $ x = 1 $
- $ a = -2 < 0 $ → opens downward
- Vertex is a maximum
- Pick $ x = 2 $: $ y = -2(1)^2 + 5 = -2 + 5 = 3 $ → Point: $ (2, 3) $
- Y-intercept: $ x = 0 $:
$ y = -2(-1)^2 + 5 = -2(1) + 5 = -2 + 5 = 3 $ → $ (0, 3) $

✔ Summary:
- Axis of Symmetry: $ x = 1 $
- Vertex: $ (1, 5) $
- Opens down? Yes
- Max or min? Maximum
- Point from vertex: $ (2, 3) $
- Y-intercept: $ (0, 3) $

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🔷 Problem 6: $ y = 3(x + 2)^2 - 2 $

- $ h = -2 $, $ k = -2 $
- Vertex: $ (-2, -2) $
- Axis of Symmetry: $ x = -2 $
- $ a = 3 > 0 $ → opens upward
- Vertex is a minimum
- Pick $ x = -1 $: $ y = 3(1)^2 - 2 = 3 - 2 = 1 $ → Point: $ (-1, 1) $
- Y-intercept: $ x = 0 $:
$ y = 3(2)^2 - 2 = 3(4) - 2 = 12 - 2 = 10 $ → $ (0, 10) $

✔ Summary:
- Axis of Symmetry: $ x = -2 $
- Vertex: $ (-2, -2) $
- Opens up? Yes
- Min or max? Minimum
- Point from vertex: $ (-1, 1) $
- Y-intercept: $ (0, 10) $

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🔷 Problem 7: $ y = -\frac{1}{4}(x - 2)^2 + 1 $

- $ h = 2 $, $ k = 1 $
- Vertex: $ (2, 1) $
- Axis of Symmetry: $ x = 2 $
- $ a = -\frac{1}{4} < 0 $ → opens downward
- Vertex is a maximum
- Pick $ x = 3 $: $ y = -\frac{1}{4}(1)^2 + 1 = -0.25 + 1 = 0.75 $ → Point: $ (3, 0.75) $
- Y-intercept: $ x = 0 $:
$ y = -\frac{1}{4}(-2)^2 + 1 = -\frac{1}{4}(4) + 1 = -1 + 1 = 0 $ → $ (0, 0) $

✔ Summary:
- Axis of Symmetry: $ x = 2 $
- Vertex: $ (2, 1) $
- Opens down? Yes
- Max or min? Maximum
- Point from vertex: $ (3, 0.75) $
- Y-intercept: $ (0, 0) $

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🔷 Problem 8: $ y = 2(x - 1)^2 + 3 $

Wait — this appears to be repeated or mislabeled. Let's check the original list.

Actually, looking at your input:

> 8) $ y = 2(x - 1)^2 + 3 $

This is identical to Problem 3, but let’s go through it again:

- $ h = 1 $, $ k = 3 $
- Vertex: $ (1, 3) $
- Axis of Symmetry: $ x = 1 $
- $ a = 2 > 0 $ → opens upward
- Vertex is a minimum
- Pick $ x = 2 $: $ y = 2(1)^2 + 3 = 2 + 3 = 5 $ → Point: $ (2, 5) $
- Y-intercept: $ x = 0 $:
$ y = 2(-1)^2 + 3 = 2(1) + 3 = 2 + 3 = 5 $ → $ (0, 5) $

✔ Summary:
- Axis of Symmetry: $ x = 1 $
- Vertex: $ (1, 3) $
- Opens up? Yes
- Min or max? Minimum
- Point from vertex: $ (2, 5) $
- Y-intercept: $ (0, 5) $

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## ✔ Final Answer Table:

| Problem | Axis of Symmetry | Vertex | Opens Up/Down | Min/Max | Point from Vertex | Y-intercept |
|--------|------------------|--------|---------------|---------|--------------------|-------------|
| 1 | $ x = 3 $ | $ (3, -4) $ | Up | Min | $ (4, -3) $ | $ (0, 5) $ |
| 2 | $ x = -1 $ | $ (-1, 2) $ | Down | Max | $ (0, 1) $ | $ (0, 1) $ |
| 3 | $ x = 4 $ | $ (4, 1) $ | Up | Min | $ (5, 3) $ | $ (0, 33) $ |
| 4 | $ x = -2 $ | $ (-2, 3) $ | Down | Max | $ (-1, 2.5) $ | $ (0, 1) $ |
| 5 | $ x = 1 $ | $ (1, 5) $ | Down | Max | $ (2, 3) $ | $ (0, 3) $ |
| 6 | $ x = -2 $ | $ (-2, -2) $ | Up | Min | $ (-1, 1) $ | $ (0, 10) $ |
| 7 | $ x = 2 $ | $ (2, 1) $ | Down | Max | $ (3, 0.75) $ | $ (0, 0) $ |
| 8 | $ x = 1 $ | $ (1, 3) $ | Up | Min | $ (2, 5) $ | $ (0, 5) $ |

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📌 How to Graph:

For each function:
1. Plot the vertex.
2. Draw the axis of symmetry as a dashed vertical line.
3. Use the point from vertex and y-intercept to plot two more points.
4. Reflect those points across the axis of symmetry.
5. Sketch the parabola accordingly (upward or downward).

Let me know if you'd like a visual sketch or help plotting these!