Convert the quadratic y=(x+5)2+1

Question

from vertex form to standard form.(1 point)
Responses

y=x2+5x+11
y is equal to x squared plus 5 x plus 11

y=x2+10x+26
y is equal to x squared plus 10 x plus 26

y=x2−4x+8
y is equal to x squared minus 4 x plus 8

y=x2+26
y is equal to x squared plus 26

Answer 1

To convert the quadratic from vertex form \( y = (x + 5)^2 + 1 \) to standard form, we will expand it.

1. Start with the vertex form:

\[ y = (x + 5)^2 + 1 \]

2. Expand \( (x + 5)^2 \):

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

3. Substitute this back into the equation:

\[ y = x^2 + 10x + 25 + 1 \]

4. Combine the constant terms:

\[ y = x^2 + 10x + 26 \]

Thus, the converted standard form is:

\[ y = x^2 + 10x + 26 \]

So, the correct response is:

y = x² + 10x + 26