Question
Complete the square for y = x^2 - 4x + 7
Answers
GPT-4o mini
To complete the square for the quadratic expression \( y = x^2 - 4x + 7 \), we follow these steps:
1. Start with the expression:
\[
y = x^2 - 4x + 7
\]
2. Focus on the quadratic and linear terms \( x^2 - 4x \). We need to complete the square for these terms. Take the coefficient of \( x \) (which is \(-4\)), divide it by 2, and then square the result:
\[
\left( \frac{-4}{2} \right)^2 = (-2)^2 = 4
\]
3. Add and subtract this square inside the expression:
\[
y = (x^2 - 4x + 4) + 7 - 4
\]
4. Now rewrite the perfect square trinomial and simplify:
\[
y = (x - 2)^2 + 3
\]
Thus, the completed square form of the equation is:
\[
y = (x - 2)^2 + 3
\]
1. Start with the expression:
\[
y = x^2 - 4x + 7
\]
2. Focus on the quadratic and linear terms \( x^2 - 4x \). We need to complete the square for these terms. Take the coefficient of \( x \) (which is \(-4\)), divide it by 2, and then square the result:
\[
\left( \frac{-4}{2} \right)^2 = (-2)^2 = 4
\]
3. Add and subtract this square inside the expression:
\[
y = (x^2 - 4x + 4) + 7 - 4
\]
4. Now rewrite the perfect square trinomial and simplify:
\[
y = (x - 2)^2 + 3
\]
Thus, the completed square form of the equation is:
\[
y = (x - 2)^2 + 3
\]