Rewrite the following quadratic functions in intercept or factored form. show your work. y = 9 + 12x + 4x^2

y = (2x + 3)(2x + 3) = (2x + 3)²

Step-by-step explanation:

We are given a quadratic function and we have to write it in factored form.

y = 9 + 12x + 4x²

y = 4x² + 12x + 9

We can break the mid-term in such a way that when they are multiplied, the factors give a product of 36x² and when added, they give a result of 12x, as show below:

y = 4x² + 6x + 6x + 9

Taking 2x common from the first two variables and 3 from the second two

y = 2x(2x + 3) + 3(2x + 3)

Taking 2x+3 common

y = (2x + 3)(2x + 3) = (2x + 3)²

Step-by-step explanation:

We are given the following the quadratic function and we are to rewrite it in intercept or factored form:

Rearranging the given function to get:

Rewriting and in as perfect squares:

Now applying the exponent rule:

Rewriting it in the form :

Here and . So the factored form is