Question

Rewrite the following quadratic functions in intercept or factored form. Show your work.

y = 9 + 12x + 4x^2

Answer 1

`(2x+3)^2`

Explanation:

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

`y = 9 + 12x + 4x^2`

Rearranging the given function to get:

`y = 4x^2+12x+9`

Rewriting
`4` and
`4` in
`y = 4x^2+12x+9` as perfect squares:

`2^2x^2+12+3^2`

Now applying the exponent rule:
`a^mb^m=(ab)^m`

`(2x)^2+12x+3^2`

Rewriting it in the form
`(a+b)^2=a^2+2ab+b^2`:

`(2x)^2+2(2x)(3)+3^2`

Here
`a=2x` and
`b=3`. So the factored form is
`(2x+3)^2`

Answer 2

y = (2x + 3)(2x + 3) = (2x + 3)²

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