Max/Min of a quadratic function/ Problem solving

[Stephxox]

So, the question is:

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

Does anybody know how to answer this

 

[stapel]

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

This is a negative quadratic, so the graph will be an "upside-down" parabola,the "maximum value" obviously being the highest point, or the vertex.

So use whatever method you've been taught for finding the vertex, and see what restrictions you have to put on k so that the values of the coordinates in the vertex are not fractions. :idea:

If you get stuck, kindly please reply with a clear listing of your work and reasoning so far, including a specification of the particular method you are using. (There are various methods; it's probably best we stick with the one you've been taught.) Thank you!

Eliz.

 

[Stephxox]

We have been taught to complete the square, however, I don`t understand how you can do that with k as variable in the question.

So far all I have is:

y= -4x2 + kx - 1
y= -4 (x2 -kx÷-4 ) -1 (divided out the -4 from the fist two terms)

then I`m stuck becuase to do the next step, you need to take half of the middle term and then square it, but I don`t know how that is possible with k in the equation.

 

[mmm4444bot]

y= -4x2 + kx - 1
y= -4 (x2 -kx÷-4 ) -1 (divided out the -4 from the fist two terms)

Hello Steph:

You did not correctly factor out the -4.

We can see this if we multiply the expression you wrote inside the parentheses by -4. Doing so results in the following equation.

y = -4x^2 - kx - 1

Clearly, this is not the same as the given equation.

Also, I would like to suggest that you write the factor inside parentheses as follows.

y = -4(x^2 - kx/4) - 1

This makes it easier to see that the coefficient on the x-term is -k/4. You need to take one-half of this coefficient and square the result.

\(\displaystyle \left( \frac{\frac{-k}{4}}{2} \right)^2 = \left( \frac{1}{2} \cdot \frac{-k}{4} \right)^2 \;=\; ?\)

Please continue from here.

Thank you very much for showing your work.

Cheers,

~ Mark