Question

Question

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

y=x2+8x+11
y is equal to x squared plus 8 x plus 11

y=x2+4x+16
y is equal to x squared plus 4 x plus 16

y=x2+3
y is equal to x squared plus 3

y=x2+11
y is equal to x squared plus 11

Answer 1

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

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

2. Expand \( (x + 4)^2 \):
   \[ (x + 4)(x + 4) = x^2 + 4x + 4 \]

3. Substitute the expansion back into the equation:
   \[ y = x^2 + 4x + 4 - 5 \]

4. Simplify the equation:
   \[ y = x^2 + 4x - 1 \]

So, the standard form of the quadratic is:
\[ y = x^2 + 4x - 1 \]

None of the provided options match this answer exactly, but if there's a mistake in the problem or options list, please clarify. If you're looking for the closest match based on the responses given, the options could be incorrect. Please double-check the options, but based on the calculation, the correct transformation leads us to:

None of the listed responses are correct.