Convert the equation from vertex form to standard form y=−4(x+5)2−3 .(1 point) Responses y=−4x2−40x−103 y equals negative 4 x squared minus 40 x minus 103 y=16x2+160x+397 y equals 16 x squared plus 160 x plus 397 y=16x2+160x+412 y equals 16 x squared plus 160 x plus 412 y=−4x2−25x−3

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.

Convert the equation from vertex form to standard form y=−4(x+5)^2−3.

Learn how to convert the quadratic equation y = −4(x+5)^2−3 from vertex form to standard form. Step-by-step explanation with expansion and simplification techniques. Suitable for Grades 8-10 students studying quadratic equations.

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