anonymous
  • anonymous
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)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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caozeyuan
  • caozeyuan
you mean -16x^2?
anonymous
  • anonymous
yea
caozeyuan
  • caozeyuan
and x-intercept means y=0, so -16x^2+22x+3=0

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anonymous
  • anonymous
yes
caozeyuan
  • caozeyuan
because 3 is prime we have (ax+3)(bx+1)=-16x^2+22x+3
anonymous
  • anonymous
how did you get that?
caozeyuan
  • caozeyuan
assume (ax+c))(bx+d)=-16x^2+22x+3
anonymous
  • anonymous
oh ok but why did you put 3 and 1 into the slots?
caozeyuan
  • caozeyuan
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
anonymous
  • anonymous
oh so when it says "What are the x-intercepts of the graph" they would be c=3,d=1?
caozeyuan
  • caozeyuan
we are not there yet, bear with me for a second
anonymous
  • anonymous
ok
caozeyuan
  • caozeyuan
now expand LHS we have ab=-16,3b+a=22
caozeyuan
  • caozeyuan
we can recoginze that 8 and -2 is plausible answer
anonymous
  • anonymous
why cause they both go into 16?
caozeyuan
  • caozeyuan
since 3b+a is 22, a is -2, b is8
caozeyuan
  • caozeyuan
sorry what is your question?
anonymous
  • anonymous
Part A: What are the x-intercepts of the graph of the f(x)? Show your work.
caozeyuan
  • caozeyuan
now since y is 0, either -2x+3 is 0 or 8x+1 is 0
caozeyuan
  • caozeyuan
I dont understand "why cause they both go into 16?"
anonymous
  • anonymous
I said that because you said 8 and 2 are possible anwser
anonymous
  • anonymous
and 8 and 2 both go into 16
caozeyuan
  • caozeyuan
ab=-16, so you want one+ and one -
anonymous
  • anonymous
yea I get that part
caozeyuan
  • caozeyuan
8 and 2 is not possible since it would give the coeffecient before x^2 16,not -16
caozeyuan
  • caozeyuan
since 3b+a=22, we want to have 24-2, so a=-2 and b is 8
anonymous
  • anonymous
I forgot it was a negative ha
caozeyuan
  • caozeyuan
So now you should have factorized the quadratic equation
caozeyuan
  • caozeyuan
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
anonymous
  • anonymous
oh ok so than what would be the anwser?
caozeyuan
  • caozeyuan
you can calculate it yourself, it is simple once you factored the quadratic eqaution
anonymous
  • anonymous
ok I got it now thanks and do you think you can help with part B and C?
caozeyuan
  • caozeyuan
sure
anonymous
  • anonymous
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
caozeyuan
  • caozeyuan
maxmium because secondary derivative is negative
caozeyuan
  • caozeyuan
d^2y/dx^2=-32
caozeyuan
  • caozeyuan
to find coord, you do first derivtive, set dy/dx=0, find, plug back in to find y
caozeyuan
  • caozeyuan
I am not sure if you finished calc I or not
caozeyuan
  • caozeyuan
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
anonymous
  • anonymous
could you just help me with part C and ill be good
caozeyuan
  • caozeyuan
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
anonymous
  • anonymous
Well you did great thanks for helping me out :)

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