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QUESTION

# How do I convert the equation f(x)=x^2-2x-3 to vertex form?

color(red)( f(x) = (x-1)^2-4)

The vertex form of a quadratic is given by y = a(x – h)^2 + k, where (h, k) is the vertex.

The "a" in the vertex form is the same "a" as in y = ax^2 + bx + c.

f(x) = x^2-2x-3

We convert to the "vertex form" by .

Step 1. Move the constant to the other side.

f(x)+3 = x^2-2x

Step 2. Square the coefficient of x and divide by 4.

(-2)^2/4 = 1

Step 3. Add this value to each side

f(x)+3+1 = x^2-2x+1

Step 4. Express the right hand side as a square.

f(x)+4 = (x-1)^2

Step 5. Isolate f(x).

f(x) = (x-1)^2-4

The equation is now in vertex form.

y = a(x – h)^2 + k, where (h, k) is the vertex.

h = 1 and k = -4, so the vertex is at (1,-4).