Question

What is the vertex of the quadratic function f(x) = (x – 8)(x + 2)?

Answer 1

Answer:

The vertex is  (3,-25)

Step-by-step explanation:

Quadratic Function has the form:

$f(x)=ax^2+bx+c$

Lets use distributive property [a(b+c)=ab+ac] to make the equation given into the vertex form. Thus, we have:

$f(x)=(x-8)(x+2)\\f(x)=x^2+2x-8x-16\\f(x)=x^2-6x-16$

Thus,

a = 1

b = -6

c = -16

The x coordinate of vertex is given as:

$x=-\frac{b}{2a}$

Putting the points, we have:

$x=-\frac{-6}{2(1)}=3$

Putting x = 3 into the function, we get y-value of vertex:

$f(x)=(x-8)(x+2)\\f(x)=(3-8)(3+2)\\f(x)=(-5)(5)\\f(x)=-25$

The vertex is  (3,-25)