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

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Answer 1 · 2015-07-29T17:41:46

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

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 $y = ax^2 + bx + c$ .

Your equation is

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

We convert to the "vertex form" by completing the square.

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 ( $1,-4$ ).

Graph 1

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