Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

25.10.2 Test (CST): Polynomial FunctionsQuestion 9 of 25Which of the two functions below has the smallest minimum .y-value?f(x) = x5-2g(x) = 3x² + 1O A. g(x)OB. There is not enough information to determineC. The y-values for f(x)and g(x) both go to -O D. f(x)SUBMIT

25102 Test CST Polynomial FunctionsQuestion 9 Of 25Which Of The Two Functions Below Has The Smallest Minimum Yvaluefx X52gx 3x 1O A GxOB There Is Not Enough Inf class=

Sagot :

Solution

- To find the minimum values of the functions, we need to find the x-value of the vertex of the quadratic function, and then subsitute this x-value into the function to get its minimum value, while for the quintic equation, we simply apply the fact that it is an odd function. Because of this, the tails of the function move in opposite directions; one towards positive infinity, while the other moves towards negative infinity.

- The formula for finding the x-value of the vertex of a quadratic function is:

[tex]x=-\frac{b}{2a},\text{ Given, }ax^2+bx+c=f(x)[/tex]

- Thus, we can find the x-value of the vertex for the quadratic equation as follows:

[tex]\begin{gathered} f(x)=3x^2+1 \\ a=3,b=0,c=1 \\ \\ \therefore x=-\frac{b}{2a}=-\frac{0}{2(3)}=0 \end{gathered}[/tex]

- Now that we have the x-value of the vertex of the quadratic equation, we can find its minimum value as follows:

[tex]\begin{gathered} f(x)=3x^2+1 \\ put\text{ }x=0 \\ f(x)=3(0)^2+1 \\ f(x)=1 \end{gathered}[/tex]

- Thus, the minimum value of the quadratic equation is 1.

- Next, we already know that the quintic equation moves down towards negative infinity. Thus f(x), the quintic equation, has a smaller minimum value

Final Answer

f(x), the quintic equation, has a smaller minimum value

Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.