1006

Note Definitions and Procedures to be Memorized

For reference: Synopsis with References to Multiple Choice
Path from Default Page: Precalculus I > Assts scroll to bottom of page then Partial Notes for Fall 2004
Note for reference: Linked Outline

At the computer, use Windows Explorer to find h:\shares\physics (you'll have to open this using Windows Explorer, which is accessed by clicking on My Computer on your desktop) and open the program Multiple Choice Questions. Using 163_core as your 'course', run the following:

Core Problems to Date

Monday we will be doing the DERIVE exercise, which you should have completed by Wednesday. You can take the Major Quiz on Monday if you haven't taken it this week.

Class Discussion centered on the slope = slope equation for a straight line, in which the slope between given points (x1, y1) and (x2, y2) is set equal to the slope between (x1, y1) and the variable point (x, y) on the line. The result is the two-point form of the equation of a straight line. The point was made that once you have the picture and understand that the two expressions for the slope must be equal, it is easy to write down the slope = slope equation and rearrange it into the two-point form. Another point is that the SOL tests cannot easily measure such graphical reasoning so it isn't tested, and therefore is not usually taught (schools have to teach what the SOL dictates; the fault lies with the design of the SOL test, not with your schools), and this sort of reasoning might therefore be new to you.

Quiz Results:

Approximately 70% of the quiz questions were answered correctly.

The table below shows questions for which the wrong answer was given by students on today's quiz. If an answer was given by more than one student then it will appear more than once.

You should be sure you understand the error that led to the incorrect answer.

Correct answer Question

n The zeros of the function y = f(t) are found by plugging 0 in for t and evaluating the function to find y.

y There are parabolic functions for which the vertex is the lowest point.

y If the graph of a quadratic function passes through the horizontal axis it does so at horizontal coordinates (-b +- sqrt(b^2 - 4 a c) ) / (2a).

y For a function y = f(t), there can be only one value of y which corresponds to t = 0.

n For a function y = f(t), there can be any number of values of y which correspond to t = 0.

y The values of y which correspond to t = c can be found by locating t = c on the horizontal axis, moving upward along the line t = c to the graph, then across to the y axis. If t is a valid value of the independent variable (i.e., if t is in the domain of the function) then there will be exactly one such point.

n The values of t for which the function y = f(t) is equal to c are found by evaluating the expression f(c).

n The equation f(t) = c might have any finite number of solutions but cannot have a infinite number.

n The values of y which correspond to t = 0 are represented by the points where the graph of the function crosses the t axis.

y The values of y which correspond to t = c can be found by locating t = c on the horizontal axis, moving upward along the line t = c to the graph, then across to the y axis.

y The values of y which correspond to t = c can be found by locating t = c on the horizontal axis, moving upward along the line t = c to the graph, then across to the y axis. If t is a valid value of the independent variable (i.e., if t is in the domain of the function) then there will be exactly one such point.

n If a data set such as [ [2, 9], [3, 12], [4, 18] ] is in line #20, then the command fit( [x, a x^2 + b x + c ] , #20) can be simplified to give you the equation of the parabola that best fits the data.

n The axis of symmetry of a quadratic function is the line x = (-b +- sqrt(b^2 - 4 a c) ) / (2 a).

y The values of y which correspond to t = c are found by plugging c in for t and evaluating the function to find y.

n The values of y which correspond to t = c can be found by locating y = c on the vertical axis, moving horizontally along the line y = c to the graph, then moving vertically to the t axis.

y To author an expression you have to get into the narrow box near the bottom of the screen.

y You can plot a data set in DERIVE using the syntax [ [2, 9], [3, 12], [4, 18] ], for example, to represent y values 9, 12 and 18 vs. x values 2, 3, 4.

y If you plot a data set such as [ [2, 9], [3, 12], [4, 18] ], three points will appear on the graph, provided that the graph has an appropriate plot range.

n If you author an equation you can click on Plot and follow a few simple steps to get the solution.

n Every point of the graph of y = f ( x - h ) lies -h units in the horizontal direction from the corresponding point of the graph of y = f(x).

n If you plot the expression (x-2)(x+3) and the expression 2x + 7, DERIVE will automatically scale the screen so you can see where the two graphs cross.

n The data set [ [2, 9], [3, 12], [4, 18] ] would be represented in DERIVE as (2, 9), (3,12), (4,18).

n If you plot a data set such as [ [2, 9], [3, 12], [4, 18] ], three points and a best-fit line will appear on the graph, provided that the graph has an appropriate plot range.

Correct answer	Question
n	The zeros of the function y = f(t) are found by plugging 0 in for t and evaluating the function to find y.
y	There are parabolic functions for which the vertex is the lowest point.
y	If the graph of a quadratic function passes through the horizontal axis it does so at horizontal coordinates (-b +- sqrt(b^2 - 4 a c) ) / (2a).
y	For a function y = f(t), there can be only one value of y which corresponds to t = 0.
n	For a function y = f(t), there can be any number of values of y which correspond to t = 0.
y	The values of y which correspond to t = c can be found by locating t = c on the horizontal axis, moving upward along the line t = c to the graph, then across to the y axis. If t is a valid value of the independent variable (i.e., if t is in the domain of the function) then there will be exactly one such point.
n	The values of t for which the function y = f(t) is equal to c are found by evaluating the expression f(c).
n	The equation f(t) = c might have any finite number of solutions but cannot have a infinite number.
n	The values of y which correspond to t = 0 are represented by the points where the graph of the function crosses the t axis.
y	The values of y which correspond to t = c can be found by locating t = c on the horizontal axis, moving upward along the line t = c to the graph, then across to the y axis.
y	The values of y which correspond to t = c can be found by locating t = c on the horizontal axis, moving upward along the line t = c to the graph, then across to the y axis. If t is a valid value of the independent variable (i.e., if t is in the domain of the function) then there will be exactly one such point.
n	If a data set such as [ [2, 9], [3, 12], [4, 18] ] is in line #20, then the command fit( [x, a x^2 + b x + c ] , #20) can be simplified to give you the equation of the parabola that best fits the data.
n	The axis of symmetry of a quadratic function is the line x = (-b +- sqrt(b^2 - 4 a c) ) / (2 a).
y	The values of y which correspond to t = c are found by plugging c in for t and evaluating the function to find y.
n	The values of y which correspond to t = c can be found by locating y = c on the vertical axis, moving horizontally along the line y = c to the graph, then moving vertically to the t axis.
y	To author an expression you have to get into the narrow box near the bottom of the screen.
y	You can plot a data set in DERIVE using the syntax [ [2, 9], [3, 12], [4, 18] ], for example, to represent y values 9, 12 and 18 vs. x values 2, 3, 4.
y	If you plot a data set such as [ [2, 9], [3, 12], [4, 18] ], three points will appear on the graph, provided that the graph has an appropriate plot range.
n	If you author an equation you can click on Plot and follow a few simple steps to get the solution.
n	Every point of the graph of y = f ( x - h ) lies -h units in the horizontal direction from the corresponding point of the graph of y = f(x).
n	If you plot the expression (x-2)(x+3) and the expression 2x + 7, DERIVE will automatically scale the screen so you can see where the two graphs cross.
n	The data set [ [2, 9], [3, 12], [4, 18] ] would be represented in DERIVE as (2, 9), (3,12), (4,18).
n	If you plot a data set such as [ [2, 9], [3, 12], [4, 18] ], three points and a best-fit line will appear on the graph, provided that the graph has an appropriate plot range.