Question

Give the vertex form of the equation that is equivalent to y = x^2 - 6x + 10.

A) y = (x - 3)^2 + 1
B) y = x^2 - 6x + 10
C) y = (x + 3)^2 - 1
D) y = (x - 6)^2 + 10

Answer 1

The vertex form of the equation that is equivalent to y = x^2 - 6x + 10 is y = (x - 3)^2 + 1.

Step-by-step explanation:

The vertex form of a quadratic equation is given by y = (x - h)^2 + k, where (h, k) represents the coordinates of the vertex. To find the vertex form of the equation y = x^2 - 6x + 10, we need to complete the square.

Step 1: Group the x terms together and complete the square:

y = (x^2 - 6x) + 10

y = (x^2 - 6x + 9) + 10 - 9

y = (x - 3)^2 + 1

Therefore, the vertex form of the equation equivalent to y = x^2 - 6x + 10 is y = (x - 3)^2 + 1 (option A).