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

y = 9 + 12x + 4x^2

Respuesta :

SaniShahbaz

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

alinakincsem

Answer:

[tex](2x+3)^2[/tex]

Step-by-step explanation:

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

[tex]y = 9 + 12x + 4x^2[/tex]

Rearranging the given function to get:

[tex]y = 4x^2+12x+9[/tex]

Rewriting [tex] 4[/tex] and [tex] 4[/tex] in [tex]y = 4x^2+12x+9[/tex] as perfect squares:

[tex]2^2x^2+12+3^2[/tex]

Now applying the exponent rule: [tex]a^mb^m=(ab)^m[/tex]

[tex](2x)^2+12x+3^2[/tex]

Rewriting it in the form [tex](a+b)^2=a^2+2ab+b^2[/tex]:

[tex](2x)^2+2(2x)(3)+3^2[/tex]

Here [tex]a=2x[/tex] and [tex]b=3[/tex]. So the factored form is [tex](2x+3)^2[/tex]



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