Question

What is the minimum value of the function f(x)=(2x+6)(x-7)

Answer 1

One way to answer this is to expand the function:

f(x) = (2x+6)(x-7)

= 2x^2 - 14x + 6x - 42

= 2x^2 - 8x - 42

And then use the formula
`x=(-b)/(2a)` to find the x-value of the vertex and then use that to find the y-value of the vertex, while is the minimum value.

x = -(-8) / 2(2)

= 8/4

= 2

f(2) = 2(2)^2 - 8(2) - 42

= 2(4) - 16 - 42

= 8 - 16 - 42

= - 50

So the minimum value is -50, since (2,-50) is the lowest point on the parabola.