Question

Put the quadratic into vertex form and state the coordinates of the vertex. y= x² – 2x – 3 Vertex Form: y = Vertex: Submit Answer

Answer 1

The Vertex form of a Quadratic equation is:

`f(x)=a\mleft(x-h\mright)^2+k`

Where the vertex of the parabola is:

`(h,k)`

Given the following Quadratic equation:

`y=x^(2)-2x-3`

You can write in Vertex form by completing the square. The steps are:

1. You need divide the coefficient of the x-term by 2, square it and add it to both sides of the equation. Notice that:

`((2)/(2))^2=1^2=1`

Then:

`y+(1)=x^(2)-2x-3+(1)`

2. Move the term to the left side:

`y+3+(1)=x^2-2x+(1)`

3. Simplifying and factoring:

`y+4=(x-1)^2`

4. Solve for "y":

`y=(x-1)^2-4`

Now you can identify that:

`\begin{gathered} h=1 \\ k=-4 \end{gathered}`

The answer is:

a. Vertex form:

`y=(x-1)^2-4`

b. Vertex:

`(1,-4)`