To solve this question, we need to convert the vertex form of the parabola:

$y = 7(x - 3)^2 + 4$

into its standard form, which is $y = ax^2 + bx + c$.

Steps:

1. Expand $(x - 3)^2$: $(x - 3)^2 = x^2 - 6x + 9$

2. Substitute this into the equation: $y = 7(x^2 - 6x + 9) + 4$

3. Distribute the 7: $y = 7x^2 - 42x + 63 + 4$

4. Simplify the constant terms: $y = 7x^2 - 42x + 67$

Final Answer:

The standard form is: $\boxed{y = 7x^2 - 42x + 67}$

Correct option: A

Would you like a detailed explanation of the steps or have any questions?

Follow-Up Questions:

1. How do you derive the vertex form of a parabola from its standard form?
2. What are the key differences between vertex and standard forms of a parabola?
3. How do changes to the $a$, $h$, and $k$ values in the vertex form affect the graph?
4. What are the characteristics of a parabola (vertex, axis of symmetry, etc.) in standard form?
5. Why is expanding and simplifying important in algebraic manipulations?

Tip:

When converting between forms, always carefully expand and combine like terms to avoid calculation errors!