Question

Give the vertex for the quadratic function: f (x) = (x – 3) (x + 7)​

Answer 1

`Vertex = (-2,-25)`

Explanation:

Given

`f(x) = (x - 3)(x + 7)`

Required

The vertex

`f(x) = (x - 3)(x + 7)`

Open bracket

`f(x) = x^2 -3x+7x-21`

`f(x) = x^2 +4x-21`

Express -21 as 4 - 25

`f(x) = x^2 +4x+4-25`

Group as:

`f(x) = (x^2 +4x+4)-25`

Factorize the expression in bracket

`f(x) = (x+2)^2-25`

The vertex form is:

`f(x) = a(x - h)^2 + k`

Where the vertex is:

`Vertex = (h,k)`

`Vertex = (-2,-25)`