What is the vertex of this equation? y=x^2-6x+4. Please show the steps on how you got the answer so i can understand it better.

x^2 - 6 x + 4 = y

subtract 4 from both sides
x^2 - 6 x = y-4
square half of 6 which is 3^2=9
add 9 to both sides
x^2 - 6 x + 9 = y + 5
factor left, perfect square now
(x-3)^2 = y + 5
vertex at (3 , -5)

To find the vertex of a quadratic equation in the form y = ax^2 + bx + c, you can use the formula x = -b/(2a) to find the x-coordinate of the vertex.

In your equation, y = x^2 - 6x + 4, we can see that a = 1, b = -6, and c = 4.

Step 1: Find the x-coordinate of the vertex.
x = -b/(2a)
= -(-6)/(2(1))
= 6/2
= 3

So, the x-coordinate of the vertex is 3.

Step 2: Substitute the x-coordinate of the vertex into the equation to find the y-coordinate.
y = (3)^2 - 6(3) + 4
= 9 - 18 + 4
= -5

So, the y-coordinate of the vertex is -5.

Thus, the vertex of the equation y = x^2 - 6x + 4 is (3, -5).

To find the vertex of the equation y = x^2 - 6x + 4, you can follow these steps:

Step 1: Identify the coefficients of the quadratic equation.

- In this equation, the coefficient of x^2 is 1, the coefficient of x is -6, and the constant term is 4.

Step 2: Use the formula to find the x-coordinate of the vertex.

- The x-coordinate of the vertex, denoted as "h", can be found using the formula h = -b/(2a), where a is the coefficient of x^2 and b is the coefficient of x.
- In this case, a = 1 and b = -6. Plugging these values into the formula, we get h = -(-6)/(2*1) = 6/2 = 3.

Step 3: Substitute the x-coordinate of the vertex into the equation to find the y-coordinate.

- Now that we have the value of h, we substitute it back into the equation to obtain the y-coordinate of the vertex.
- Plugging in h = 3, we get y = (3)^2 - 6(3) + 4 = 9 - 18 + 4 = -5.

Step 4: Write down the vertex.

- The vertex is represented as (h, k), where h is the x-coordinate and k is the y-coordinate.
- Using the values we obtained, the vertex of the equation y = x^2 - 6x + 4 is (3, -5).

Therefore, the vertex of the given equation is (3, -5).