Question

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

Answer 1

y = x^2 - 12 x + 7
y = x^2 - 12 x + 6^2 ... - 6^2 + 7
y = x^2 - 12 x + 36 - 29
y = (x-6)^2 - 29
therefore symmetric about the veritcal line x = 6
and hits that line at y = -29

Answer 2

To write the expression in vertex form, we need to complete the square by adding and subtracting a constant term inside the parentheses.
First, we need to factor out the coefficient of 𝑥2, which is 1 in this case:

𝑦 = 𝑥2 − 12𝑥 + 7
= (𝑥 − 6)2 − 36 + 7 (since (a-b)^2 = a^2 -2ab + b^2, we can add and subtract (6)^2=36 inside the parentheses)
= (𝑥 − 6)2 − 29

Therefore, the vertex form of the expression 𝑦 = 𝑥2 − 12𝑥 + 7 is 𝑦 = (𝑥 − 6)2 − 29 . The vertex is at (6, -29).

Answer 3

Yes, that's correct! Great job!