y=-3(x+5)^2-4 convert the equation from vertex form to standard form

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: \( (a + b)^2 = a^2 + 2ab + b^2 \).

Learn how to convert the quadratic equation y=-3(x+5)^2-4 from vertex form to standard form. This step-by-step guide covers key algebraic concepts such as binomial expansion, the distributive property, and simplifying terms. Ideal for students in Grades 9-11.

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