Step by Step explanation of Vertex Form of f(x)=x^2-6x-40

A quadratic in vertex form reads as

(x - a)² + b

where (a, b) is the vertex.

To get the given quadratic in this form, complete the square:

x² - 6x - 40 = x² - 6x + 9 - 49 = (x - 3)² - 49

Or, work backwards by expanding the vertex form and solving for a and b :

(x - a)² + b = x² - 2ax + a² + b

So if

x² - 6x - 40 = x² - 2ax + a² + b,

then

-2a = -6   →   a = 3

a² + b = -40   →   b = -49

i hope this is what you were looking for.

see attached graph

113.1

step-by-step explanation:

v=4

3πr3=4

3·π·33≈113.09734