To convert the quadratic equation $y = -3(x + 5)^2 - 4$ from vertex form to standard form, follow these steps:

Step 1: Expand the squared term

Start with the equation: $y = -3(x + 5)^2 - 4$ Expand $(x + 5)^2$: $(x + 5)^2 = (x + 5)(x + 5) = x^2 + 10x + 25$ Now substitute this back into the equation: $y = -3(x^2 + 10x + 25) - 4$

Step 2: Distribute the -3

Distribute the $-3$ to each term inside the parentheses: $y = -3x^2 - 30x - 75 - 4$

Step 3: Combine like terms

Now combine the constants: $y = -3x^2 - 30x - 79$

Final answer (Standard form):

The standard form of the equation is: $y = -3x^2 - 30x - 79$

Would you like further details on the process or have any questions?

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Here are 5 related questions to deepen your understanding:

1. How would you find the vertex of a quadratic equation in standard form?
2. Can you identify the axis of symmetry from the vertex form equation?
3. How does the coefficient of $x^2$ affect the shape of the parabola?
4. What are the steps to convert a standard form equation back to vertex form?
5. How would you determine the roots of the equation from its standard form?

Tip: When expanding binomials like $(x + 5)^2$, always use the distributive property or the square of a binomial formula: $(a + b)^2 = a^2 + 2ab + b^2$.