Question

Plz help for a medal:
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)

Answer 1

you mean -16x^2?

Answer 2

yea

Answer 3

and x-intercept means y=0, so -16x^2+22x+3=0

Answer 4

yes

Answer 5

because 3 is prime we have (ax+3)(bx+1)=-16x^2+22x+3

Answer 6

how did you get that?

Answer 7

assume (ax+c))(bx+d)=-16x^2+22x+3

Answer 8

oh ok but why did you put 3 and 1 into the slots?

Answer 9

now, obvious cd=3, but 3 is prime which means the only possible answer is c=3,d=1, the other way round is the same, not a different answer

Answer 10

oh so when it says "What are the x-intercepts of the graph" they would be c=3,d=1?

Answer 11

we are not there yet, bear with me for a second

Answer 12

ok

Answer 13

now expand LHS we have ab=-16,3b+a=22

Answer 14

we can recoginze that 8 and -2 is plausible answer

Answer 15

why cause they both go into 16?

Answer 16

since 3b+a is 22, a is -2, b is8

Answer 17

sorry what is your question?

Answer 18

Part A: What are the x-intercepts of the graph of the f(x)? Show your work.

Answer 19

now since y is 0, either -2x+3 is 0 or 8x+1 is 0

Answer 20

I dont understand "why cause they both go into 16?"

Answer 21

I said that because you said 8 and 2 are possible anwser

Answer 22

and 8 and 2 both go into 16

Answer 23

ab=-16, so you want one+ and one -

Answer 24

yea I get that part

Answer 25

8 and 2 is not possible since it would give the coeffecient before x^2 16,not -16

Answer 26

since 3b+a=22, we want to have 24-2, so a=-2 and b is 8

Answer 27

I forgot it was a negative ha

Answer 28

So now you should have factorized the quadratic equation

Answer 29

since y=0, either the first factor is 0 or the second, set them each to 0 and solve for x, thats your x intercept

Answer 30

oh ok so than what would be the anwser?

Answer 31

you can calculate it yourself, it is simple once you factored the quadratic eqaution

Answer 32

ok I got it now thanks and do you think you can help with part B and C?

Answer 33

sure

Answer 34

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) @caozeyuan

Answer 35

maxmium because secondary derivative is negative

Answer 36

d^2y/dx^2=-32

Answer 37

to find coord, you do first derivtive, set dy/dx=0, find, plug back in to find y

Answer 38

I am not sure if you finished calc I or not

Answer 39

well, a parabola is defined by 3 non collinear points, the two intercepts and the vertex are the three points, so yes it can be graphed

Answer 40

could you just help me with part C and ill be good

Answer 41

I am not sure about the standad steps, but I would draw a vertical line down to x axis from the vertex,this is the symmetry line of parabola, then connncet left intercept with vertex and right interest with vertex, make sure two curves are smooth and symmetrical

Answer 42

Well you did great thanks for helping me out :)