Rewrite the quadratic function in the form that best reveals the zeros of the function: f (x) = 2 (2x^2+4x) + 3

f (x) = ?

Step-by-step explanation:

The given quadratic function is f (x) = 2 (2x^2+4x) + 3

Multiplying through to open the brackets,

f (x) = 4x^2 + 8x + 3

To find the zeros, we will equate

f (x) = 0

Therefore,

4x^2 + 8x + 3 = 0

Finding two numbers such that when we multiply them, it gives us 12xx^2 and when we add them, it gives us 8x, we have 6x and 2x. Therefore,

4x^2 + 8x + 3 = 0 is expressed as

4x^2 + 2x + 6x + 3 = 0

2x (2x + 2) + 3 (2x + 3) = 0

(2x + 2) (2x + 3) = 0

f (x) = 2x + 2) (2x + 3)