Question

Write the following expression in vertex form by completing the square. 𝑦 = 𝑥2 − 12𝑥 + 7

Answer 1

To complete the square, we need to take half of the coefficient of the x-term and square it. Then, we can add and subtract this value inside the parentheses containing the x-terms in the quadratic.

First, let's factor out any common factor from the x-terms:

𝑦 = 𝑥^2 − 12𝑥 + 7
𝑦 = 1(𝑥^2 − 12𝑥) + 7

Now, we can see that the coefficient of the x-term is -12, so we need to add and subtract (12/2)^2 = 36 inside the parentheses:

𝑦 = 1(𝑥^2 − 12𝑥 + 36 - 36) + 7
𝑦 = 1(𝑥 - 6)^2 - 29

So the vertex form of the equation is y = (𝑥 - 6)^2 - 29.