## anonymous one year ago What are the coordinates of the vertex for f(x) = 2x2 + 4x + 9? (−2, 4) (−1, 7) (1, 15) (2, 9)

1. Nnesha

formula to find x coordinate of vertex $\huge\rm x=\frac{ -b }{ 2a }$

2. Nnesha

then substitute all x in f(x) equation for its value to find y-coordinate of vertex

3. anonymous

what do i put for the a and b?

4. Nnesha

a=leading coefficient b=middle term $\huge\rm \color{reD}{A}x^2+\color{blue}{B}x+C=0$

5. anonymous

ok thank you

6. anonymous

do i leave the negative sign in front of the b even when it's a positive?

7. Nnesha

yes b is positive but negative is in the formula so that stays there

8. anonymous

so it would be $x=\frac{ -4 }{ 2(2)}$?

9. Nnesha

yep right

10. anonymous

so -4/4 and i would just divide it and it would come out as -1 right?

11. Nnesha

yes that's x-coordinate

12. anonymous

how do i find the y-coordinate now?

13. Nnesha

now to find y -coordinate substitute x for -1 $\rm \color{reD}{x=-1}$ $\huge\rm 2\color{reD}{x}^2+4\color{red}{x}+9=0$

14. anonymous

so the y-coordinate would be 3? (-1,3)?

15. Nnesha

mhm

16. Nnesha

when you take square of negative number you will get positive number

17. anonymous

how do i do that

18. Nnesha

$\huge\rm 2\color{reD}{(-1)}^2+4\color{red}{(-1)}+9=0$ now solve (-1)^2 is same as -1 times -1 = ?

19. anonymous

so 1?

20. Nnesha

yes -1 times -1 = 1 (-1)^2=1 so solve $\huge\rm 2\color{reD}{(1)}+4\color{red}{(-1)}+9=?$

21. anonymous

oh so (-1,7)

22. Nnesha

yep

23. anonymous

could you help me out with another one

24. anonymous

@Nnesha

25. Nnesha

i'll try

26. anonymous

What is the equation of the quadratic graph with a focus of (5, −1) and a directrix of y = 1? f(x) = −one fourth (x − 5)2 + 1 f(x) = one fourth (x − 5)2 + 1 f(x) = −one fourth (x − 5)2 f(x) = one fourth (x − 5)2

27. anonymous

@Nnesha ?

28. Nnesha

29. Nnesha

sorry

30. anonymous

its fine. i got it Cx thank you tho !

31. Nnesha

np