anonymous
  • anonymous
can someone help me!!??? please i would really appreciate it. question: If y=-4x²+kx-1determine the value(s) of k for which the maximum value of the function is an integer. Explain your reasoning using pictures, numbers, and words.
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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amistre64
  • amistre64
lets try this from the quad formula perspective... sqrt(k^2 -4(-1)(-4)) would have to be equal to or greater than 0
amistre64
  • amistre64
k^2 -16 >= 0 k^2 >= 16 k >= +-sqrt(16) k>= -4, or 4
amistre64
  • amistre64
or rather k>= |4 ro -4|...might be a better scenario :)

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amistre64
  • amistre64
since -4x^2 gives us an upsode down "U" for a graph, we can determine the "largest value"... at the vertex: -k/2(-4)
amistre64
  • amistre64
-k/-8 = k/8 we have some value for "x" which is equal to k/8 can we use that in our equation?
amistre64
  • amistre64
y=-4(k/8)²+k(k/8)-1 y = -4k^2/61 + k^2/8 - 1
amistre64
  • amistre64
61 = 64 in my world lol
amistre64
  • amistre64
y = -4k^2/64 + 8k^2/64 -1 y = 4k^2/64 - 1 y = 4k^2/64 - 1 y = k^2/16 - 1 can we do anything with this "value"?
amistre64
  • amistre64
or am I making this to hard on myself....
amistre64
  • amistre64
-4x^2 +kx -1 = 0 factors to.. 4x^2 -kx +1 = 0 1,4 = 4 2,2 = 4 (x- 1)(4x- 1) or (2x-1) (2x-1)
amistre64
  • amistre64
k=5.... i beieve
anonymous
  • anonymous
how??
amistre64
  • amistre64
the values we get for the product of "ac" are: 4(1) = 4 1+4 = 5, k=5 in this instance 2+2 = 4, k=4 in this instance. but I might have a "sign" out of place so I would have to recheck it all :) but does that make sense?
anonymous
  • anonymous
can we do this from the beginning again??
anonymous
  • anonymous
if y=-4x^2 +k -1 dont we plug it into the discriminant?
anonymous
  • anonymous
a=-4 b=k c=-1
amistre64
  • amistre64
which beginning :) I was trying to determine a good manner in which to appraoch the problem...the discriminate there was not an "easy" way.... that I could see.
anonymous
  • anonymous
i mean from the beggining of the question...so far thats what i know
anonymous
  • anonymous
but the question states tht the value of the function is an integer so does tht mean that the value of k <0
amistre64
  • amistre64
its easier to approach from the "meaing" that is given to a,b, and c the "c" term is a product of 2 numbers; the "b" term is a sum of 2 numbers. for "b" to have the greatest value, the sum of the factors of "c" would have to combine to the biggest value right?
anonymous
  • anonymous
i have no idea what u just said?? lol
amistre64
  • amistre64
an integer is any number between -infinity and +infinity... :)
anonymous
  • anonymous
ooo okay...
amistre64
  • amistre64
the bigest integer value can p[ossibly be a negative value as long as it is the biggest integer we can get :)
amistre64
  • amistre64
but lets try this approach... first we factor out that -1 to make our lives easier: y = -1(4x^2 -kx +1) we good here?
anonymous
  • anonymous
okay..
amistre64
  • amistre64
we need to gather a "pool" of options for the middle term. that "pool" comes from the number we get when we multiply "a" and "c". 4 times 1 = 4. we good so far?
anonymous
  • anonymous
wait when u r doing this r u plugging it into the discriminant??? or just doing it...?
amistre64
  • amistre64
just doing it.... the discrimant is only valueable if you "know" what k is.... so lets continue on this path and see where it leads :)
amistre64
  • amistre64
we need two number: call them "m" and "n", that multiply together to get "4" and ADD together to get our value for "k". does that make sense?
anonymous
  • anonymous
yes ur doing product n sum
amistre64
  • amistre64
correct: our options are: 4(1) = 4; 4+1 = 5 2(2) = 4; 2+2 = 4 which number is greater.... 4 or 5?
anonymous
  • anonymous
the 2(2) seems reasonable..cuz u need greates common factor right??
amistre64
  • amistre64
we couldnt care less about "common" factors here :) what we care about is the greatest value that we can get for "k". the value for "k" is obtained by "adding together" the factors that make up "4". That is our only concern :)
anonymous
  • anonymous
so if we r looking for the greatest common value then we use the numbers 1 n 4...
anonymous
  • anonymous
i mean the greatest value for k
amistre64
  • amistre64
thats right.... so lets see if 5 is a good answer by plugging it into our original formula and seeing what we get:) y = -4x^2 +(5)x - 1 how would we TEST this situation?
anonymous
  • anonymous
if y =0??
amistre64
  • amistre64
our "highest point" is at our vertex: -b/2a -5/2(-4) = -5/-8 = 5/8 5/8...our "vertex is at 5/8. what is the value of y at x = 5/8?
anonymous
  • anonymous
where did u get -b/2a?
amistre64
  • amistre64
that is from the quadratic formula as well.... do you know the quadratic formula?
anonymous
  • anonymous
yes
anonymous
  • anonymous
i didnt tht it gives u the highest point at the vertex..
anonymous
  • anonymous
i dint know
amistre64
  • amistre64
the quad formula says that the roots of a quadratic expression are equal distances from a certain value of x.... right? -b sqrt(b^2-4ac) --- + or - ------------- 2a 2a right?
anonymous
  • anonymous
yes
amistre64
  • amistre64
so the cernter, or vertex, of our equation lies between these 2 points..... the x value of our "vertex" then must be -b/2a.... am I right?
amistre64
  • amistre64
if you move 5 feet to your left, or 5 feet to your right.... where is the middle of that?.... exactly where you were standing to begin with right?
amistre64
  • amistre64
-sqrt(b^2-4ac).......-b.......+sqrt(b^2-4ac) ------------ --- ------------- 2a 2a 2a I hope this displays correctly lol
amistre64
  • amistre64
does that make sense?
anonymous
  • anonymous
yupp
anonymous
  • anonymous
i think i got it thanks i think i can handle it from here
anonymous
  • anonymous
thanks for ur help
amistre64
  • amistre64
ok :) but if this might clarify things a bit
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