Question

What is the vertex of `y= 2x^2 -4x - 12`?

Answer 1

Vertex`" "->" "(x,y)=(1,-14)`

Explanation:

I am going to use part of the process of completing the square.

Write as:`" "y=2(x^2-4/2x)-12`

`x_("vertex")=(-1/2)xx(-4/2) = + 1`

So by substitution:

`y_("vertex")=2(1)^2-4(1)-12 = -14`

Vertex`" "->" "(x,y)=(1,-14)`

Answer 2

The vertex is `=(1,-14)`

Explanation:

We need

`a^2-2ab+b^2=(a-b)^2`

Let complete the squares and factorise

`y=2x^2-4x-12`

`y=2(x^2-2x)-12`

`y=2(x^2-2x+1)-12-2`

`y=2(x-1)^2-14`

Therefore,

the vertex is `=(1,-14)`

graph{(y-(2x^2-4x-12))((x-1)^2+(x+14)^2-0.01)=0 [-7.8, 6.25, -14.32, -7.295]}