Parabola Review Worksheet | mrmillermath - Free Printable

Let's analyze each parabola on the worksheet and identify its vertex, minimum/maximum value, domain, range, and zeros (x-intercepts). We'll go through them one by one.

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1. First Parabola (Top Left)

- Shape: Opens upward (U-shaped).
- Vertex: The lowest point of the parabola.
- From the graph: It appears at (1, -4).
- Min/Max: Since it opens upward → Minimum at vertex.
- So, Minimum = -4
- Domain: All real numbers (parabolas extend infinitely left and right).
- Domain: $(-\infty, \infty)$
- Range: Starts at the minimum y-value and goes up.
- Range: $[-4, \infty)$
- Zeros: Where the graph crosses the x-axis.
- The parabola crosses the x-axis at x = -1 and x = 3.
- So, Zeros: $x = -1$, $x = 3$

✔ Answer for #1:
- Vertex: (1, -4)
- Min/Max: Minimum = -4
- Domain: $(-\infty, \infty)$
- Range: $[-4, \infty)$
- Zeros: -1, 3

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2. Second Parabola (Top Right)

- Shape: Opens downward (inverted U).
- Vertex: Highest point.
- From graph: Appears at (-2, 4).
- Min/Max: Opens downward → Maximum at vertex.
- So, Maximum = 4
- Domain: All real numbers.
- Domain: $(-\infty, \infty)$
- Range: From maximum down to negative infinity.
- Range: $(-\infty, 4]$
- Zeros: Crosses x-axis at x = -4 and x = 0.
- So, Zeros: $x = -4$, $x = 0$

✔ Answer for #2:
- Vertex: (-2, 4)
- Min/Max: Maximum = 4
- Domain: $(-\infty, \infty)$
- Range: $(-\infty, 4]$
- Zeros: -4, 0

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3. Third Parabola (Bottom Left)

- Shape: Opens downward.
- Vertex: Highest point.
- From graph: At (1, 5).
- Min/Max: Opens downward → Maximum = 5
- Domain: All real numbers.
- Domain: $(-\infty, \infty)$
- Range: From max down.
- Range: $(-\infty, 5]$
- Zeros: Crosses x-axis at x = -1 and x = 3.
- So, Zeros: $x = -1$, $x = 3$

✔ Answer for #3:
- Vertex: (1, 5)
- Min/Max: Maximum = 5
- Domain: $(-\infty, \infty)$
- Range: $(-\infty, 5]$
- Zeros: -1, 3

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4. Fourth Parabola (Bottom Right)

- Shape: Opens upward.
- Vertex: Lowest point.
- From graph: At (0, -2).
- Min/Max: Opens upward → Minimum = -2
- Domain: All real numbers.
- Domain: $(-\infty, \infty)$
- Range: From minimum up.
- Range: $[-2, \infty)$
- Zeros: Crosses x-axis at x = -1 and x = 1.
- So, Zeros: $x = -1$, $x = 1$

✔ Answer for #4:
- Vertex: (0, -2)
- Min/Max: Minimum = -2
- Domain: $(-\infty, \infty)$
- Range: $[-2, \infty)$
- Zeros: -1, 1

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✔ Final Answers Summary:

| Problem | Vertex | Min/Max | Domain | Range | Zeros |
|--------|------------|----------------|------------------|--------------------|----------------|
| 1 | (1, -4) | Minimum = -4 | $(-\infty, \infty)$ | $[-4, \infty)$ | -1, 3 |
| 2 | (-2, 4) | Maximum = 4 | $(-\infty, \infty)$ | $(-\infty, 4]$ | -4, 0 |
| 3 | (1, 5) | Maximum = 5 | $(-\infty, \infty)$ | $(-\infty, 5]$ | -1, 3 |
| 4 | (0, -2) | Minimum = -2 | $(-\infty, \infty)$ | $[-2, \infty)$ | -1, 1 |

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🔍 Explanation of Concepts:

- Vertex: The turning point of the parabola (peak or valley).
- Min/Max: If opens up → minimum; if opens down → maximum.
- Domain: All possible x-values → always $(-\infty, \infty)$ for parabolas.
- Range: All possible y-values → depends on vertex and direction.
- Zeros (x-intercepts): Points where the graph crosses the x-axis (y = 0).

Let me know if you'd like this formatted as a printable answer sheet!