Find k so y = -4x^2+kx-1 has integer for max value

1. The question asks you for what values of k would yield a maximum value that's an integer. Wouldn't that be your answer?

2. Again, the question asks you for what values of k gives you one root. Wouldn't that be your answer?
 
Markus said:
You just lost me... Im soo confused! Why is there a k/8 on the left side? The equation is not yx...
are you not familiar with function notation?

y(k/8) is the same thing as f(k/8), i.e., the function value when x = k/8 ... it is not y times x.
 
So my final answer for number 1 would be:
y=-4(x²-k/4x)-1
=-4(x²-k/4x + k/64) -1 +4(k/64)
=-4(x-k/8)² + (k²/4-1)
= 4

And for number two i would have:
b²-4ac
=(-k)²-4(1)(k+8)
=k²-4k-32
=(k-8)(k+4)
.....what do i put for my final answer?
 
Markus said:
So my final answer for number 1 would be:
y=-4(x²-k/4x)-1
=-4(x²-k/4x + k/64) -1 +4(k/64)
=-4(x-k/8)² + (k²/4-1)
= 4

no, that is not correct

And for number two i would have:
b²-4ac
=(-k)²-4(1)(k+8)
=k²-4k-32
=(k-8)(k+4)
.....what do i put for my final answer?

the values of k that make b<sup>2</sup>-4ac = 0
 
Ugh why is it wronge? What did i do wronge? And for the second do you mean 8 and -4? But the question only asks for the value of k
 
Markus said:
Ugh why is it wronge? What did i do wronge? And for the second do you mean 8 and -4? But the question only asks for the value of k
I gave you the "answer" to the first problem earlier. "4" by itself does not answer the question.

As far as the second problem goes ... did you ever bother to think that more than one value of k might work?
 
Yes i did but the question does not say it in plural like the other one does do i figured it only asked for one number. But so we all agree that the answer for number to is:

k= 8, -4

Ohh and for the first question would the answer be:
x=-b/(2a)
=-k/(2*-4)
= k/8
y(k/8) = -4(k/8)² + k(k/8) - 1
= -k²/16 + k²/8 - 1
= k²/16 - 1
= (k/4)² - 1
.:. the value for k is the integer 4
 
Markus said:
Okay thanks so much for taking the time to read this.

Here is the questions that i cannot do:

1. If y=-4x²+kx-1, determine the value(s) for k which the maximum value of a function is an integer. Explain your reasoning.

2. The graph of the function f(x) = x²-kx+k+8 touches the x-axis at one point. What is the value of k?

I need this asap! Thanks sooo much!

Value(s) - means it could be plural or singular.
 
...yes i already knew that thanks. Can someone please tell me if i have the right answer? Thanks.
 
Markus said:
...so we all agree that the answer for number [two] is: k= 8, -4

Ohh and for the first question would the answer be...the integer 4
If this is your answer then it is wrong.
 
okay but can you please help me and tell me what is wrong about it. what am i doing wrong why cant anyone just help me out!
 
You already found the answer. All k = all integers that are multiples of 4. If k = 4, -16, 20, etc. it'll give an integer value.

And for the second question, there ARE two values for k even though the question did not specifically ask for it.
 
Markus said:
...yes i already knew that thanks. Can someone please tell me if i have the right answer? Thanks.
You've been given "the right answers", and you are apparently so lost that, even after lengthly explanations, complete set-ups and fully-worked solutions, you aren't apparently even aware that these answers have been provided. :shock:

I truly regret that you're so very "lost" on this material; I'm afraid this thread evidences a need for in-depth and face-to-face tutoring. Please seriously consider hiring a local qualified tutor, and setting aside a few hours a week for diligent re-teaching. Your local high school (guidance office or math department) or college (tutoring office or math department) should be able to provide you with some good leads. :idea:

My best wishes to you! :D

Eliz.
 
By the way, to consolidate what you've been given:

1) If y = -4x<sup>2</sup> + kx - 1, determine the value(s) for k which the maximum value of a function is an integer. Explain your reasoning.
You've been told that the maximum of a negative quadratic is the vertex of the corresponding downward-opening parabola. So you need to learn about quadratics, graphing parabolas, and finding vertices.

You've been given the formula for the vertex of a parabola. For f(x) = y = ax<sup>2</sup> + bx + c, the vertex (h, k) is at h = -b/(2a), with k = f(h). So you need to learn how to work with variables, formulas, and function notation.

(Note: The "k" in the vertex formula is not the same "k" as in your exercise. So I'll use "K" in what follows for the vertex-formula "k".)

For this particular exercise, you were given that the maximum value occurs at:

. . . . .h = -k/(2(-4)) = -k/-8 = k/8

This was further explained, step-by-step, to mean that the maximum value is:

. . . . .K = f(h) = -4(k/8)<sup>2</sup> + k(k/8) - 1

. . . . .= -4(k<sup>2</sup>/64) + k<sup>2</sup>/8 - 1

. . . . .= -k<sup>2</sup>/16 + k<sup>2</sup>/8 - 1

. . . . .= k<sup>2</sup>/16 - 1

. . . . .= (k/4)<sup>2</sup> - 1

For this to be a whole-number value, it was explained to you that k has to be divisible evenly by 4, so as to avoid fractions. Since k/4 is squared, of course k could be positive or negative, so the solution, as was provided to you earlier, is "k is any multiple of 4".

(Your tutor can teach you how "k = ±4m for any integer m" means the same thing as the above solution, as you are probably expected to understand this more-technical form).

2. The graph of the function f(x) = x²-kx+k+8 touches the x-axis at one point. What is the value of k?
You were given that the "touching at one point" means that the discriminant of the Quadratic Formula for x<sup>2</sup> - kx + (k + 8) must be equal to zero. So you need to learn how to use the Quadratic Formula, and how to "set things equal to zero".

In this case, you were given the quadratic function:

. . . . .f(x) = x<sup>2</sup> - kx + (k + 8)

You were instructed to find the discriminant of the Quadratic Formula symbolically, and were told to use a = 1, b = -k, and c = k + 8:

. . . . .Let x<sup>2</sup> - kx + (k + 8) = 0

. . . . .discriminant: b<sup>2</sup> - 4ac

. . . . .(-k)<sup>2</sup> - 4(1)(k + 8) = 0

. . . . .k<sup>2</sup> - 4k - 32 = 0

. . . . .(k - 8)(k + 4) = 0

It was then explained that you need to solve the above to find the values of k:

. . . . .k - 8 = 0 or k + 4 = 0

. . . . .k = 8 or k = -4

You were then told that this was the answer.

When you work with your tutor, please print out the various solutions, explanations, and links you'd been given, so you can work together with him to figure these out.

Good luck! :D

Eliz.
 
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