Question
A)Convert the quadratic y=(x+5)2+1y=(x+5)2+1 from vertex form to standard form.(1 point) Responses y=x2+5x+11
Answers
GPT-4o mini
To convert the quadratic equation \( y = (x + 5)^2 + 1 \) from vertex form to standard form, we will first expand the expression.
1. Start with the vertex form:
\[ y = (x + 5)^2 + 1 \]
2. Expand \( (x + 5)^2 \):
\[ (x + 5)(x + 5) = x^2 + 10x + 25 \]
3. Now substitute back into the equation:
\[ y = x^2 + 10x + 25 + 1 \]
4. Combine the constants:
\[ y = x^2 + 10x + 26 \]
So, the standard form of the quadratic equation is:
\[ y = x^2 + 10x + 26 \]
The response you provided \( y = x^2 + 5x + 11 \) is incorrect. The correct standard form is \( y = x^2 + 10x + 26 \).
1. Start with the vertex form:
\[ y = (x + 5)^2 + 1 \]
2. Expand \( (x + 5)^2 \):
\[ (x + 5)(x + 5) = x^2 + 10x + 25 \]
3. Now substitute back into the equation:
\[ y = x^2 + 10x + 25 + 1 \]
4. Combine the constants:
\[ y = x^2 + 10x + 26 \]
So, the standard form of the quadratic equation is:
\[ y = x^2 + 10x + 26 \]
The response you provided \( y = x^2 + 5x + 11 \) is incorrect. The correct standard form is \( y = x^2 + 10x + 26 \).