Convert the equation from vertex form to standard form y=−4(x+5)^2 − 3 .(1 point)

Question

Responses

y=−4x^2 − 40x−103
y equals negative 4 x squared minus 40 x minus 103

y=−4x^2 −25x−3
y equals negative 4 x squared minus 25 x minus 3

y=16x^2 +160x+412
y equals 16 x squared plus 160 x plus 412

y=16x^2+160x+397

Answer 1

To convert the equation from vertex form \( y = -4(x + 5)^2 - 3 \) to standard form, we need to expand the equation.

1. Start with the given equation: \[ y = -4(x + 5)^2 - 3 \]

2. Expand \( (x + 5)^2 \): \[ (x + 5)^2 = x^2 + 10x + 25 \]

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

4. Distribute \(-4\): \[ y = -4x^2 - 40x - 100 - 3 \]

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

So, the equivalent standard form is: \[ y = -4x^2 - 40x - 103 \]

Thus, the correct response is: y = −4x^2 − 40x − 103.