Quadratic equations in vertex, standard, and factored forms for multiple options.

It looks like you've uploaded a table of quadratic equations, labeled from B to F, with each row containing three different forms of quadratic functions: vertex form, standard form, and factored form. However, there's no explicit task or question stated in your message.

But based on the format, it seems likely that this is part of a matching or identification exercise—perhaps asking you to:

- Match equivalent quadratic equations across different forms (e.g., vertex, standard, factored),
- Identify key features (like vertex, roots, axis of symmetry),
- Or determine which equations represent the same parabola.

Since you didn't specify the actual task, I'll assume a common type of problem: Match the equivalent quadratic expressions in each row (B through F) — meaning, for each row, verify that all three equations are algebraically equivalent.

Let’s go through each row and check whether the three expressions are equivalent.

---

🔹 Row B:

1. $ y = -4(x - 2)^2 + 64 $
2. $ y = -4x^2 + 16x + 48 $
3. $ y = -4(x + 2)(x - 6) $

#### Step 1: Expand expression 1
$$
y = -4(x - 2)^2 + 64 = -4(x^2 - 4x + 4) + 64 = -4x^2 + 16x - 16 + 64 = -4x^2 + 16x + 48
$$
✔ Matches expression 2.

#### Step 2: Expand expression 3
$$
y = -4(x + 2)(x - 6) = -4[(x)(x - 6) + 2(x - 6)] = -4[x^2 - 6x + 2x - 12] = -4(x^2 - 4x - 12)
$$
$$
= -4x^2 + 16x + 48
$$
✔ Matches both others.

✔️ Row B: All three are equivalent.

---

🔹 Row C:

1. $ y = -5(x - 3)(x + 1) $
2. $ y = -5(x - 1)^2 + 20 $
3. $ y = -5x^2 + 10x + 15 $

#### Step 1: Expand expression 1
$$
y = -5(x - 3)(x + 1) = -5[x^2 + x - 3x - 3] = -5(x^2 - 2x - 3) = -5x^2 + 10x + 15
$$
✔ Matches expression 3.

#### Step 2: Expand expression 2
$$
y = -5(x - 1)^2 + 20 = -5(x^2 - 2x + 1) + 20 = -5x^2 + 10x - 5 + 20 = -5x^2 + 10x + 15
$$
✔ Matches both.

✔️ Row C: All three are equivalent.

---

🔹 Row D:

1. $ y = -2(x - 4)^2 + 32 $
2. $ y = -2x(x - 8) $
3. $ y = -2x^2 + 16x $

#### Step 1: Expand expression 1
$$
y = -2(x - 4)^2 + 32 = -2(x^2 - 8x + 16) + 32 = -2x^2 + 16x - 32 + 32 = -2x^2 + 16x
$$
✔ Matches expression 3.

#### Step 2: Expand expression 2
$$
y = -2x(x - 8) = -2x^2 + 16x
$$
✔ Matches both.

✔️ Row D: All three are equivalent.

---

🔹 Row E:

1. $ y = -2(x - 7)(x + 3) $
2. $ y = -2x^2 + 8x + 42 $
3. $ y = -2(x - 2)^2 + 50 $

#### Step 1: Expand expression 1
$$
y = -2(x - 7)(x + 3) = -2[x^2 + 3x - 7x - 21] = -2(x^2 - 4x - 21) = -2x^2 + 8x + 42
$$
✔ Matches expression 2.

#### Step 2: Expand expression 3
$$
y = -2(x - 2)^2 + 50 = -2(x^2 - 4x + 4) + 50 = -2x^2 + 8x - 8 + 50 = -2x^2 + 8x + 42
$$
✔ Matches both.

✔️ Row E: All three are equivalent.

---

🔹 Row F:

1. $ y = -3x^2 + 21x $
2. $ y = -3(x - 3.5)^2 + 36.75 $
3. $ y = -3x(x - 7) $

#### Step 1: Expand expression 3
$$
y = -3x(x - 7) = -3x^2 + 21x
$$
✔ Matches expression 1.

#### Step 2: Expand expression 2
$$
y = -3(x - 3.5)^2 + 36.75
$$
Note: $ 3.5 = \frac{7}{2} $, so:
$$
(x - 3.5)^2 = x^2 - 7x + 12.25
$$
Then:
$$
y = -3(x^2 - 7x + 12.25) + 36.75 = -3x^2 + 21x - 36.75 + 36.75 = -3x^2 + 21x
$$
✔ Matches both.

✔️ Row F: All three are equivalent.

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✔ Final Answer:

All rows (B through F) contain three equivalent quadratic equations in different forms.

Each row represents the same parabola written in:
- Vertex form,
- Standard form,
- Factored form.

So if the task was to verify equivalence, then the answer is:

> ✔ All equations in each row are algebraically equivalent.

If you had a specific task (e.g., "Find the vertex", "Find the roots", "Graph", etc.), please clarify, and I can help further!