Which polynomial function can be represented by the graph below

Mathematics

1 answer:

s344n2d4d5 [400]2 years ago

8 0

<u>Answer:</u>

The correct answer option is C. $f(x)=-2x^3-2x^2+12x$ .

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

From the given graph of the polynomial function, we can see that the graph passes through the following points: $(-3,0), (0,0)$ and $(2,0)$ .

So the roots or zeros of this polynomial function are: $-3,0$ and $2$ .

Now, we'd graph the equation of the given polynomial and will check for roots and end behavior of the graph.

Therefore, the polynomial function that is represented by the graph is:

$f(x)=-2x^3-2x^2+12x$

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If f(x-3)=x^2-4x+5, what's f(1-x)

olganol [36]

Answer:

$\large\boxed{f(1-x)=x^2-4x+5}$

Step-by-step explanation:

$f(x-3)=x^2-4x+5\\\\f((x-3)+3)\to\text{put x + 3 to the equation of the function:}\\\\f(x-3+3)=(x+3)^2-4(x+3)+5\\\text{use the distributive property and}\ (a+b)^2=a^2+2ab+b^2\\f(x)=x^2+2(x)(3)+3^2+(-4)(x)+(-4)(3)+5\\f(x)=x^2+6x+9-4x-12+5\qquad\text{combine like terms}\\f(x)=x^2+(6x-4x)+(9-12+5)\\f(x)=x^2+2x+2\\\\f(1-x)\to\text{put 1 - x to the equation of the funtion f(x):}\\\\f(1-x)=(1-x)^2+2(1-x)+2\\\text{use the distributive property and}\ (a-b)^2=a^2-2ab+b^2$