Convert the quadratic y=(x+4)2−5

Question

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

Answer 1

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

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

2. Expand \( (x + 4)^2 \): \[ = x^2 + 8x + 16 \]

3. Now, substitute back into the equation: \[ y = x^2 + 8x + 16 - 5 \]

4. Simplify the expression: \[ y = x^2 + 8x + 11 \]

Thus, the standard form of the quadratic is: \[ \boxed{y = x^2 + 8x + 11} \]