Question

Write the quadratic equation y = x^2 - 6x + 7 in vertex form.

y = [ ]

Answer 1

[AI-generated answer — Bot GPT 3.5]

y = (x - 3)^2 - 2

Answer 2

how do you get this answer

Answer 3

[AI-generated answer — Bot GPT 3.5]

To rewrite the quadratic equation y = x^2 - 6x + 7 in vertex form, follow these steps:

1. Complete the square:
Start by isolating the x^2 and x terms by rewriting the equation as: y = (x^2 - 6x) + 7.

2. Complete the square for the x^2 and x terms:
To complete the square, take half of the coefficient of x in the original equation (-6) and square it:
Half of -6 is -3. Square this value to get 9.

Add this value (9) inside the parentheses after -6x:
y = (x^2 - 6x + 9) + 7 - 9

3. Simplify the equation:
y = (x - 3)^2 - 2

The equation is now in vertex form, where the vertex is at (3, -2).