Question

f(x)=(x+6)(x-4) which of the following is an equivalent form of the function f above in which the minimum value of f appears as a constant or coefficient F(x)=x^2-24F(x)=x^2+2x-24F(x)=(x-1)^2-21F(x)=(x+1)^2-25

Answer 1

f(x) = (x+6)(x-4)

Applying distributive property:

f(x) = x*x - x*4 + 6*x - 6*4

f(x) = x² + 2x - 24

The x-coordinate of the vertex is:

h = -b/(2a) = -2/(2*1) = -1

The y-coordinate of the vertex is:

k = f(h) = (-1)² + 2(-1) - 24 = 1 - 2 - 24 = -25

f(x) in vertex form is:

f(x) = a(x - h)² + k

f(x) = (x +1)² - 25

In this form, the minimum value of f (its vertex) appears as a constant or coefficient.