## anonymous one year ago An expression is shown below: f(x) = –16x2 + 22x + 3 Part A: What are the x-intercepts of the graph of the f(x)? Show your work. (2 points) Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work. (3 points) Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph. (5 points)

1. anonymous

@Australopithecus

2. anonymous

campbell_st

3. anonymous

@campbell_st

4. anonymous

@Keigh2015

5. anonymous

can you help??

6. Keigh2015

I am sorry this type of math is not my strong suit.

7. Keigh2015

@misssunshinexxoxo can you help this person with their math?

8. anonymous

its okay

9. anonymous

Hi

10. misssunshinexxoxo
11. campbell_st

well you need to factor the equation start with factoring out the negative... $f(x) = -(16x^2 - 22x - 3)$ next multiply 16 and - 3 so -48 find the factors of -48 that add to -22 the larger factor is negative its a relatively easy pair to find...

12. anonymous

i got −(8x+1)(2x−3)

13. campbell_st

that's correct so so to find the x-intercepts you need to solve 8x + 1 = 0 and 2x - 3 = 0 what values do you get...?

14. anonymous

one minute

15. anonymous

-1\8 and 3\2

16. anonymous

thats what i got

17. campbell_st

ok so that's good now part B is it a maximum or minimum...?

18. campbell_st

you need to look at the sign of the leading coefficient

19. anonymous

i have no clue @campbell_st

20. triciaal

do you know what the coefficient is?

21. campbell_st

what is the leading term in the equation..?

22. anonymous

-16 ?

23. campbell_st

so if its positive then you have a minimum, if its negative you have a maximum

24. anonymous

oooh

25. campbell_st

great so which do you have, max or min...?

26. anonymous

its both ??

27. anonymous

-1\8 is max and and 3\2 in min >??

28. campbell_st

no if the leading coefficient is negative... do you have a max or min,,, it can't be both

29. campbell_st

here is the equation $f(x) = -16x^2 + 22x + 3$ you said the leading coefficient is -16 that's correct... so if its a potive value you have a minimum if its negative you have a maximum so which do you choose

30. anonymous

max

31. campbell_st

great... now the vertex

32. campbell_st

the easiest way is to find the line of symmetry do you know about that...?

33. anonymous

no

34. triciaal

|dw:1437335587120:dw|

35. anonymous

ookay

36. campbell_st

ok the standard form of a quadratic is $0 = ax^2 + bx + c$ the line of symmetry is found using $x = \frac{-b}{2 \times a}$ in your question you have a = -16 and b = 22 you need to substitute the values into the equation to find x, the line of symmetry

37. anonymous

1116

38. anonymous

-11\16

39. anonymous

@campbell_st

40. campbell_st

nearly x = 11/16 originally it was -22/-32 so you have the x value for the vertex, now substitute that value into the original equation to get the y value in the vertex...

41. anonymous

umm

42. anonymous

idk

43. campbell_st

so its $f(11/16) = -16 \times (11/16)^2 + 22 \times (11/16) + 3$ you need to calculate this value...

44. anonymous

idk

45. anonymous

i hate this question, its so hard

46. anonymous

@campbell_st

47. campbell_st

ok.... I have to go anyway.

48. anonymous

okay