Question
convert the quadratic y=(x+5)^2 + 1 from vertex form to standard form
Answers
GPT-4o mini
To convert the quadratic equation \( y = (x + 5)^2 + 1 \) from vertex form to standard form, we start by expanding the expression.
1. Expand \( (x + 5)^2 \):
\[
(x + 5)^2 = x^2 + 10x + 25
\]
2. Now, substitute this back into the original equation:
\[
y = x^2 + 10x + 25 + 1
\]
3. Combine like terms:
\[
y = x^2 + 10x + 26
\]
Thus, the standard form of the quadratic equation is:
\[
y = x^2 + 10x + 26
\]
1. Expand \( (x + 5)^2 \):
\[
(x + 5)^2 = x^2 + 10x + 25
\]
2. Now, substitute this back into the original equation:
\[
y = x^2 + 10x + 25 + 1
\]
3. Combine like terms:
\[
y = x^2 + 10x + 26
\]
Thus, the standard form of the quadratic equation is:
\[
y = x^2 + 10x + 26
\]