Question

Which of the following is the vertex of the quadratic equation `y = 6x^2 – 24x + 32`?

Answer 1

Vertex`->(x,y)=(2,8)`

Explanation:

The method used is part way to completing the square plus anticipating part of the final stage.

Write as:`" "y=6(x^2-24/6x)+32`

`x_("vertex")=(-1/2)xx(-24/6) = 2`
Thus by substitution we have:

`y_("vertex")=6(2)^2-24(2)+32`

`y_("vertex")=8`