Question

If f(x) = (2x + 1)(2x + 3), complete the square and determine the minimum or maximum value of the function

Answer 1

Explanation:

Use FOIL, first outside inside last

2x × 2x = 4x^2

2x × 3 = 6x

1 × 2x = 2x

1 × 3 = 3

`4 {x}^(2) + 8x + 3`

The formula to find the minimum or maximum value is

`x = ( - b)/(2a)`

And remember it's always ax^2 + bx + c

So now just plug in the numbers

`( - 8)/(2(4))`

-8/8 = -1

If a > 0 then the graph is upwards, in this case 4>0 so it is upwards. And -1 is the vertex, which is the minimum value