To convert the equation from vertex form to standard form, we follow these steps.

The vertex form is:

$y = -4(x + 5)^2 - 3$

Step 1: Expand the squared term

$(x + 5)^2 = x^2 + 10x + 25$

Step 2: Multiply by $-4$

$-4(x^2 + 10x + 25) = -4x^2 - 40x - 100$

Step 3: Add the constant $-3$

$y = -4x^2 - 40x - 100 - 3$

Step 4: Simplify the constants

$y = -4x^2 - 40x - 103$

Thus, the standard form of the equation is:

$y = -4x^2 - 40x - 103$

Answer:

y = -4x² - 40x - 103

This corresponds to the first option.

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Would you like more detailed steps, or do you have any questions about the process?

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Here are 5 related questions for you:

1. How do you convert from standard form to vertex form?
2. What is the significance of the vertex in the vertex form of a quadratic equation?
3. Can you identify the axis of symmetry for the equation $y = -4x^2 - 40x - 103$?
4. How can you find the vertex of a parabola given in standard form?
5. What happens to the graph of a quadratic equation when the coefficient of $x^2$ is negative?

Tip: When converting from vertex form to standard form, always start by expanding the square and then distribute any coefficients before combining like terms.