Quadratic expressions / modelling from data

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kcharlton

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Dec 17, 2006
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1) Explain the significance of the constants m, n, and p in the completed square form of the equation y = m(x + n)^2 + p

My answer: I think they're the slope (gradient) and intercept.

2) Plot the following points on a graph:

Code: 
t  0   5  10  15  20  25  30  35  40  45  50  
s 25  31  38  43  47  47  45  41  36  30  24
Plot the points on a graph, and use the completed square form to find an equation to model the above data. Test the accuracy of your model. Use an appropriate software package to find a quadratic expression to model the data.

I've done the graphing part, but I'm needing help with the modelling part. I don't know how to do the testing part. I've used Excel as my "software package" and have gotten the expression.
 
What exactly do you want to do?. Complete the square form the quadratic you found?. If so, what is the quadratic you found?
 
y=m[x+n]^2 +P

[usually written as: y=p[x-a]^2+b]

y=m[x+n)^2+P a parabola
m positive,open up.... m negative, open down
vertex at -n,P
axis of symmetry x=-n

Arthur
all equations having squared terms are conic sections
 
1) A quadratic doesn't have a slope; slope is a characteristic of straight lines.

Try looking up this formula in your text, and seeing how it is defined. (Hint: Look at the vertex.)

2) Take your graphed points, and rough in a parabola that, to your eye, appears to pass through (or by) those points best.

From your parabola, find the vertex. Plug that into the completed-square (that is, the vertex) form of the quadratic. Then pick a point that you think is on your graph (you're eyeballing a picture, so this is all guess-work), and plug that into the formula. Solve for the value of the leading coefficient (called "m" in your text).

Now do the graph of your formula, and see how well it matches the points they gave you. And compare that graph to the one from the quadratic expression that Excel gave you.

Eliz.
 
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