Show all steps to determine the vertex for y = x2 - 6x+2

Vertex of the given equation is (3,-7).

Step-by-step explanation:

We have given a quadratic equation in standard form.

y = x²-6x+2

We have to find the vertex of the given equation.

y = (x-h) ²+k is the vertex form of the given equation where (h, k) is the vertex of the equation.

Adding and subtracting (-3) ² from given equation.

y = x²-6x + (-3) ²+2 - (-3) ²

Making formula: (a-b) ² = a²-2ab+b²

y = (x-3) ²+2-9

y = (x-3) ²-7

Comparing above equation with vertex form, we have

h = 3 and k = - 7

Hence, vertex of the given equation is (3,-7).