Question

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

Answer 1

Vertex is at `(2, -4)`

Explanation:

`color(red)(x_(vertex) = -b/(2a)) ;color(blue)( y_(vertex) = f(-b/(2a))` given the equation in the standard form of `ax^2 + bx+c`

Given :`y = x^2 - 4x + 0`

`a= 1, b = -4 , c= 0`

`color(red)(x_(vertex)) = (-(-4))/(2*1) = 4/2 = color(red)(2)`

`color(blue)(y_(vertex))= f(2) = (2)^2-4(2) = 4-8 =color(blue)(-4)`

Vertex : `(x, y) = (2, -4)`

graph{x^2-4x [-6.43, 7.62, -5.635, 1.39]}