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)

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