Mth 163
On the quiz there is a question that asks for the full statement of the Quadratic Formula. Is this just asking for -b + or - sqrt of b^2-4ac over 2a? Is this what the question is asking?
In the very first worksheet, entitle Overview, the Flow Model, Summaries of the Modeling Process, you find the statement
The quadratic formula is contained in the following statement, which you are required to know verbatim:
If y = a x^2 + bx + c, then y = 0 if, and only if, x = [ -b +- `sqrt(b^2 - 4ac) ] / (2a).
The main statement is in boldface.
You are supposed to know this statement verbatim.
Another question that I have is that one problem states: Sketch a graph representing the linear function family y=mx=b for m=.62, with b varying over all positive real numbers. How can someone sketch a graph like this with b varying over ALL real numbers? Wouldn't that involve an infinite number of integers, not to mention an infinite amount of time to do? Are you wanting the part above the original line to be blacked in?
Just as you can represent the set of counting numbers as {1, 2, 3, ... } or the set of integers as { ..., -3, -2, -1, 0, 1, 2, 3, ... } you can represent an infinite number of lines.
Recall that m is the slope and b is the y intercept of the straight line. For this family m remains constant at m = .62, so all graphs will have slope .62, therefore all will also be parallel.
I would recommend first sketching a set of coordinate axes, marking off the y intercepts for b values -3, -2, -1, 0, 1, 2, 3 (the y intercept is, again, the value of b, so you would just mark off -3, -2, ..., 3 on the y axis), and sketching a line with slope .62 through each y intercept.
To sketch a line with slope .62, start from the y axis, move over 1 unit and up .62 units. Depending on your graph scale, you might prefer to move over 10 units and up 6.2 units. Either way the graph will 'rise' .62 units for every unit of 'run' and will therefore have slope .62.
At this point you have a series of parallel lines, intercepting the y axis between -3 and +3. To indicate that this process continues forever, you could then place a series of three dots above the highest and three dots below the lowest of your graphs. To indicate that the graph includes all possible lines and not just those with integer intercepts, you could draw a series of lighter lines in between.