Question

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

Answer 1

Answer:

$Vertex = (-2,-25)$

Step-by-step 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:

$Vertex = (h,k)$

$Vertex = (-2,-25)$