What is Y equals X to the second power minus 6X + 7 in vertex form

Y = x² - 6x + 7

Vertex form is y = a (x-h) ² + k

The vertex form of this equation would be y = (x-3) ² - 2 because if we transform to the standard form it would be equal to y = x²-6x+7 so we just have to complete the perfect square (which means to complete, following the rules, with the numbers that will make this equation right in the standard form).

How our x² is equal to 1 on our standard form (like it is not 2x², it is just x²), our ''a'' on the vertex form is 1 so we simply don't have to write the 1 in front of it so it stays y = 1 (x-3) ² - 2 or y = (x-3) ²-2. Look how it works: (x-3) ² we use the rule of a²+2ab+c² which is the square of the first x² plus two times the first term times the second - 6x plus the square of the last term (-3) ² = 9 so we have x²-6x+9 - 2 that gives us the standard form x²-6x+7. So, that's true that the vertex form is y = (x-3) ²-2