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# Quadratic functions Completing the square help asap watch

1. Hey,

Im stuck on this question, where am i going wrong because I cant get the answer to equal 0

A demand curve for peanuts is represented by a section of the quadratic:

P(Q) = -Q^2 - 8Q + 84

Complete the square of this quadratic function. Use this result with explanation to (i) sketch the function (ii) suggest values for Q for which this might be a sensible demand curve.

P(Q) = -Q^2 - 8Q + 84

P(Q) = -Q^2 - 8Q + 84 = 0

(-Q^2 - 8x + 16) + 84 - 16 = 0

(-Q-4) (-Q-4) + 68 = 0

(-Q-4)^2 = -68

square root: (-Q-4)^2 = + or - square root: (-68)

-Q-4 = + or - -68

-Q-4= -68(+4) ______________-Q-4 = 68(-4)

=-64 or 64

thanks
2. It would be easier to complete the square on . Your method for completing the square looks more complicated than it needs to be... the idea is that if you have , then you halve the coefficient of and put it inside the bracket which gets squared, and then remove the square of it; so . Applying this here gives . This gives you information about an upside-down version of the graph (i.e. a reflection in the x-axis), so you can multiply both sides by -1 to give you the right-way-up version.
3. sorry, but im lost in what you are saying.

x -1 by both sides? Wouldn't that just give you the same answer?
4. What I mean by on both sides is that what you end up with by following my steps is when what you want is .

As for what you did, for some reason you have 84-16 = 68 when you should have 84+16 = 100. You somehow have also managed to get that , which isn't true, and you've made a few more arithmetical errors here and there... for example you square-rooted a negative, and after that somehow the square-root disappeared on the next line.

The equation you should end up with is , which is fairly easy to solve since 100 is a perfect square, and is positive
5. Ohh i see thanks.

So the final answer is when q =4, 100
6. (Original post by stem01)
Ohh i see thanks.

So the final answer is when q =4, 100
Well that's not the answer really...

The answer to part (i) is a plot of the graph. To do that you can use the information in the equation to find out where the vertex is, which in this case is at the point (-4, 100), and you can solve it to find out where it crosses the Q-axis, which is at the points (6, 0) and (-14, 0)... if you don't know how I got any of these answers ask me and I'll go through it.

For part (ii) you have to say which region gives sensible answers. Well, I'm assuming that Q is the number of peanuts and P(Q) is the demand for them. If so, the number of peanuts can't be negative (because that'd be silly), so Q > 0. Also, the demand for peanuts can't be less than zero either, so P(Q) > 0, meaning that -14 < Q < 6 (because outside of this region the curve crosses the Q-axis and P(Q) becomes negative). Combining the two, we get just . Again, if you don't know how I worked this out, ask me.

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