Write the following expression in vertex form by completing the square

Question

y= 𝑥2 − 12𝑥 + 7.

Answer 1

To complete the square, we need to take half of the coefficient of x, square it, and add it to both sides of the equation.

First, let's factor out the leading coefficient of 1:

y = 1(𝑥2 - 12𝑥) + 7

To complete the square, we need to add (12/2)^2 = 36 to both sides:

y = 1(𝑥2 - 12𝑥 + 36) - 36 + 7

y = 1(𝑥 - 6)2 - 29

So the vertex form of the equation is:

y = (𝑥 - 6)2 - 29

Therefore, the vertex is at (6, -29) and the parabola opens upwards.