## mathmath333 one year ago functions

1. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{Find the minimum value of the function}\hspace{.33em}\\~\\ & f(x)=\log_{2} (x^2-2x+5) \hspace{.33em}\\~\\ \end{align}}

2. anonymous

IDK

3. anonymous

make roots of the equation then use both roots to find the answer

4. misty1212

unlikely since you cannot take the log of zero

5. misty1212

find the minimum value of the quadratic

6. mathmath333

roots are imaginary here

7. misty1212

which will be the second coordinate of the vertex

8. misty1212

vertex of $x^2-2x+5$ should be easy enough to find

9. misty1212

since log is an increasing function, once you find the minimum value of the quadratic, that will give you the input that produces the minimum value of the log

10. mathmath333

minimum is 5

11. misty1212

no it is not

12. misty1212

the second coordinate of the vertex is not 5, the constant is 5

13. mathmath333

i put x=0 here x^2-2x+5

14. misty1212

yeah sure, if you put in 0 you get 5, but the vertex is NOT $$(0,5)$$

15. misty1212

use $-\frac{b}{2a}$ to find the first coordinate of the vertex

16. ganeshie8

whats the minimum value of $$x^2 - 10000000x + 1$$ ?

17. misty1212

plug that in to find the second coordinate ( it is definitely not 5)

18. anonymous

yes

19. anonymous

misty its girl like u that i study maths u are eaiutiful

20. misty1212

thank you darling, you look pretty cute yourself

21. ganeshie8

i should change my profile pic

22. mathmath333

oh i remember that dy/dx=0, minimum is 4

23. misty1212

lol pick a cute girl, everyone will love you

24. anonymous

btw can u explain it with solutionj plz

25. misty1212

yeah min is 4 and $\log_2(4)$ is your answer

26. anonymous

wait let me search cute girl pics damn those are some fine kittens

27. misty1212

you certainly don't need to use calc to find the vertex of a quadratic though...