Question

What is the vertex of `y=2x^2 -12x+23`?

Answer 1

`(3,5)`

Explanation:

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

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))`
where (h ,k) are the coordinates of the vertex and a is a constant.

`"Rearrange " y=2x^2-12x+23" into this form"`

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

`y=2(x^2-6x+23/2)`

`color(white)(y)=2((x^2-6xcolor(red)(+9))color(red)(-9)+23/2)`

`color(white)(y)=2((x-3)^2+5/2)`

`color(white)(y)=2(x-3)^2+5larrcolor(red)" in vertex form"`

`"here " h=3" and "k=5`

`rArr"vertex" =(3,5)`
graph{2x^2-12x+23 [-16.02, 16.02, -8.01, 8.01]}