Question

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

Answer 1

`y = (x-2)^2 - 16`

Explanation:

The standard form of a quadratic function is `y = ax^2+bx+c`

the equation here `y = x^2-4x-12 color(black)(" is of this form ")`

by comparison : a = 1 , b = -4 and c = -12

The vertex form of the quadratic function is

`y = a(x-h)^2 + k`
where (h , k ) are the coords of the vertex.

the x-coord of the vertex = `-b/(2a) = -(-4)/2 = 2`
substitute x = 2 into original function for y-coord.

y = `(2)^2 - 4(2) -12 = 4 - 8 - 12 = -16`
hence (h , k )= (2 , -16 ) and a = 1

`rArr y = (x - 2 )^2 - 16`
graph{x^2-4x-12 [-40, 40, -20, 20]}