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Question

Question
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

Answer 1

To convert the equation from vertex form to standard form, we start with the given vertex form equation:

\[ y = -4(x + 5)^2 - 3 \]

We can expand this equation step by step.

1. First, expand the squared term: \[ (x + 5)^2 = x^2 + 10x + 25 \]

2. Substitute this back into the equation: \[ y = -4(x^2 + 10x + 25) - 3 \]

3. Distribute \(-4\) across the terms in the parentheses: \[ y = -4x^2 - 40x - 100 - 3 \]

4. Combine the constant terms: \[ y = -4x^2 - 40x - 103 \]

Thus, the standard form of the equation is:

\[ y = -4x^2 - 40x - 103 \]

From the given responses, the correct answer is:

y = −4x² − 40x − 103