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nekit [7.7K]
3 years ago
6

The graph represents the function f(x) = x2 + 3x + 2.

Mathematics
1 answer:
Vladimir [108]3 years ago
3 0
Reflection of a function 
S_x f(x)\rightarrow{-f(x)} reflection of f(x) about x-axis

So 
g(x)=-(x^2+3x+2)=-x^2-3x-2
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NEED HELP
Zina [86]

Answer:

\displaystyle \frac{1}{2}(x^3-2x^2-5x+6)

Step-by-step explanation:

<u>Polynomials </u>

a)

The polynomial whose graph is shown is of third degree because it has three real roots. The roots of a polynomial are the values of x that make the expression equal to zero. We can see it happens three times in the graph provided. The roots or zeros are  

x=-2, x=1, x=3

b)

The factored form of a polynomial whose roots x_1, x_2, x_3 are known is

a(x-x_1)(x-x_2)(x-x_3)

We know the value of the roots, thus the polynomial is written as

a(x+2)(x-1)(x-3)

We need to find the value of a. We do that by replacing the value of x=0 and finding a that makes f(0)=3 (as seen in the graph). Thus

a(0+2)(0-1)(0-3)=3

a(2)(-1)(-3)=3

a(6)=3

\displaystyle a=\frac{3}{6}

\displaystyle a=\frac{1}{2}

Thus the factored form of the polynomial is

\displaystyle \frac{1}{2}(x+2)(x-1)(x-3)

c)

Let's multiply all the factors

\displaystyle \frac{1}{2}(x+2)(x-1)(x-3)

\displaystyle \frac{1}{2}(x^2+2x-x-2)(x-3)

\displaystyle \frac{1}{2}(x^2+x-2)(x-3)

\displaystyle \frac{1}{2}(x^3-3x^2+x^2-3x-2x+6)

\boxed{ \displaystyle \frac{1}{2}(x^3-2x^2-5x+6)}

7 0
4 years ago
A video game was $34. This weekend the game will be marked 12 percent off. How much is the game this weekend?
Angelina_Jolie [31]

Answer:

4.08$

Step-by-step explanation:

You take 12 percent of 34 which is 4.08

4 0
3 years ago
How much would $100 invested at 8% intrest compounded annually be worth after 15 years? round your answer to the nearest cent. d
frosja888 [35]
Our P = 100, r = .08, n = 1 (annually means once a year), and t = 15.  Filling in accordingly, we have A(t)=100(1+ \frac{.08}{1})^{(1)(15)}.  Simplifying a bit gives us  A(t)=100(1+.08)^{15}  and  A(t)=100(1.08)^{15}.  Raising that number inside the parenthesis to the 15th power gives us  A(t)=100(3.172169114).  Multiplying to finish means that A(t) = $317.22
3 0
4 years ago
How do I completely factor 4x^2-64?
Salsk061 [2.6K]
4x^2 - 64

= 4(x + 4) (x - 4)


4 0
3 years ago
Read 2 more answers
Plz help me get the answer ASAP
ad-work [718]

Answer:

<h2>c ≤ 4</h2>

Step-by-step explanation:

\dfrac{-1}{2}c-1\geq-3\qquad\text{add 1 to both sides}\\\\-\dfrac{1}{2}c\geq-2\qquad\text{change the signs}\\\\\dfrac{1}{2}c\leq2\qquad\text{multiply both sides by 2}\\\\c\leq4

8 0
3 years ago
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