How do you find the vertex of a parabola y=2x^2 -12x+23?

1 Answer
Jul 8, 2015

The easiest way is (probably) to convert the given equation into vertex form.
The vertex is at (3,5)

Explanation:

Vertex form of a parabola is
color(white)("XXXX")y =m(x-a)^2+b with its vertex as (a,b)

y = 2x^2-12x+23
color(white)("XXXX")extract the m
y = 2(x^2-6x) +23
color(white)("XXXX")complete the square
y = 2(x^2-6x+9) + 23 -2(9)
color(white)("XXXX")simplify into vertex form
y=2(x-3)^2 + 5

Since this is in vertex form, we can read the vertex directly from the equation as (3,5)