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3 years ago

Factor the following trinomial completely 3x^2+12x+12

1 answer:

8 0

Factor the following:
3 x^2 + 12 x + 12
Factor 3 out of 3 x^2 + 12 x + 12:
3 (x^2 + 4 x + 4)
The factors of 4 that sum to 4 are 2 and 2. So, x^2 + 4 x + 4 = (x + 2) (x + 2):
3 (x + 2) (x + 2)
(x + 2) (x + 2) = (x + 2)^2:
Answer: 3 (x + 2)^2

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Transform the given quadratic function into vertex form f(x) = quadratic function into vertex form f(x) = quadratic function int

melisa1 [442]

Answer:

Vertex form: $f(x) =(x +\frac{7}{2})^2 -\frac{53}{4}$

The vertex is $(-\frac{7}{2},-\frac{53}{4})$

Step-by-step explanation:

For a general quadratic function the form is:

$ax ^ 2 + bx + c$

For the function

$f(x) = x ^ 2+ 7x -1$

The values of the coefficients for the function are the following: $a = 1$ , $b =7$ , $c = -1$

Take the value of b and divide it by 2. Then, the result obtained squares it.

$\frac{b}{2}= \frac{7}{2}$

$(\frac{b}{2})^2=(\frac{7}{2})^2=\frac{49}{4}$

Add and subtract $\frac{49}{4}$

$f(x) = (x ^ 2 +7x +\frac{49}{4}) -\frac{49}{4}- 1$

Write the expression of the form

$f(x) = (x+\frac{b}{2})^2 +k$

$f(x) =(x +\frac{7}{2})^2 -\frac{53}{4}$

The vertex is $(-\frac{7}{2},-\frac{53}{4})$

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3 years ago

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Answer:

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Step-by-step explanation:

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Answer:

A. {x | x < 8}

Step-by-step explanation:

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x - 2 < 6

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x - 2 + 2 < 6 + 2

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3 years ago