Question

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

Answer 1

Answer:

$(2x+3)^2$

Step-by-step explanation:

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

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

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

Answer:

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