Question

What is the axis of symmetry and vertex for the graph `y=x^(2)-2x-15`?

Answer 1

`x=1" and " (1,-16)`

Explanation:

Use the method of `color(blue)"completing the square"`

`• " add " (1/2" coefficient of x-term")^2`

`"that is " ((-2)/2)^2=1`

`rArry=(x^2-2xcolor(red)(+1))color(red)(-1)-15`

`rArry=(x-1)^2-16`

The equation in `color(blue)"vertex form"` is.

`• y=a(x-h)^2+k` where `(h,k)` are the coordinates of the vertex.

`"here " h=1" and " k=-16`

`rArr" vertex " =(1,-16)`

The axis of symmetry passes through the vertex and is vertical.

`rArr"axis of symmetry is " x=1`
graph{(y-x^2+2x+15)(y+1000x-1000)=0 [-65.85, 65.85, -32.8, 33.05]}