Graphs of Parabolas - Vertex Form | PDF - Free Printable

Let’s solve each problem one by one. Each equation is in vertex form:
y = a(x - h)² + k

From this, we can find:
- Vertex: (h, k)
- Direction of opening: If a > 0, opens up; if a < 0, opens down.
- Minimum/Maximum value: If opens up → minimum at y = k; if opens down → maximum at y = k.
- Y-intercept: Plug in x = 0 and solve for y.

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Problem 21: y = -(x + 3)² - 1

Rewrite to match vertex form:
y = -1(x - (-3))² + (-1)

→ Vertex: (-3, -1)
→ a = -1 → opens down
→ Since it opens down, there’s a maximum value at y = -1
→ Y-intercept: plug in x = 0
  y = -(0 + 3)² - 1 = -(9) - 1 = -10

✔ Answer for 21:
Vertex: (-3, -1), Opens: Down, Max Value: -1, Y-intercept: (0, -10)

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Problem 22: y = -(x - 5)² + 1

Already in vertex form:
→ Vertex: (5, 1)
→ a = -1 → opens down
→ Maximum value: y = 1
→ Y-intercept: x = 0
  y = -(0 - 5)² + 1 = -(25) + 1 = -24

✔ Answer for 22:
Vertex: (5, 1), Opens: Down, Max Value: 1, Y-intercept: (0, -24)

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Problem 23: y = -(x - 1)² + 1

→ Vertex: (1, 1)
→ a = -1 → opens down
→ Maximum value: y = 1
→ Y-intercept: x = 0
  y = -(0 - 1)² + 1 = -(1) + 1 = 0

✔ Answer for 23:
Vertex: (1, 1), Opens: Down, Max Value: 1, Y-intercept: (0, 0)

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Problem 24: y = -(x + 1)² + 1

Rewrite: y = -1(x - (-1))² + 1
→ Vertex: (-1, 1)
→ a = -1 → opens down
→ Maximum value: y = 1
→ Y-intercept: x = 0
  y = -(0 + 1)² + 1 = -(1) + 1 = 0

✔ Answer for 24:
Vertex: (-1, 1), Opens: Down, Max Value: 1, Y-intercept: (0, 0)

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Problem 25: y = -(x + 2)² + 1

Rewrite: y = -1(x - (-2))² + 1
→ Vertex: (-2, 1)
→ a = -1 → opens down
→ Maximum value: y = 1
→ Y-intercept: x = 0
  y = -(0 + 2)² + 1 = -(4) + 1 = -3

✔ Answer for 25:
Vertex: (-2, 1), Opens: Down, Max Value: 1, Y-intercept: (0, -3)

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Problem 26: y = -(x + 5)²

Rewrite: y = -1(x - (-5))² + 0
→ Vertex: (-5, 0)
→ a = -1 → opens down
→ Maximum value: y = 0
→ Y-intercept: x = 0
  y = -(0 + 5)² = -(25) = -25

✔ Answer for 26:
Vertex: (-5, 0), Opens: Down, Max Value: 0, Y-intercept: (0, -25)

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Final Answer:

21) Vertex: (-3, -1), Opens: Down, Max: -1, Y-int: (0, -10)
22) Vertex: (5, 1), Opens: Down, Max: 1, Y-int: (0, -24)
23) Vertex: (1, 1), Opens: Down, Max: 1, Y-int: (0, 0)
24) Vertex: (-1, 1), Opens: Down, Max: 1, Y-int: (0, 0)
25) Vertex: (-2, 1), Opens: Down, Max: 1, Y-int: (0, -3)
26) Vertex: (-5, 0), Opens: Down, Max: 0, Y-int: (0, -25)