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Dennis_Churaev [7]
3 years ago
15

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

Mathematics
2 answers:
puteri [66]3 years ago
4 0

<u>Answer:</u>

(2x+3)^2

<u>Step-by-step explanation:</u>

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



Vlad [161]3 years ago
3 0

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

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