Download Jonathan Butturini and Connor Bliss Chapter 1 Review

Jonathan Butturini and Connor Bliss
Chapter 1 Review, Presentation, and Problems 1 and 4
Problem Number 1:
Z (E,F)
(0,0) X
J
C
Y (2,-8)
Part I: The Median
1) First, use the midpoint formula:
to find the midpoint of XY:
2) Then, the definition of slope:
to find the slope of the line passing through Z and J, the midpoint of XY:
3) Finally, use the formula:
to find an equation in terms of E and F for your final answer:
Part II: The Altitude
1) First, use the definition of slope:
to find the slope of XY:
2) Then, because a perpendicular line is the negative reciprocal of the line it crosses, the slope of Z to C
is:
3) Finally, use the formula:
to find an equation in terms of E and F for the altitude and your final answer:
NOTE: An alternative to working these problems out by hand is to use the calculator programs created
at the beginning of the semester.
Problem Number 4:
1) Here are the values given to you in order to create a quadratic equation:
Time in Seconds
Height in feet off the ground
4
147
5
103
6
27
2) Establish the equation for a projectile in feet per second is because -4.9 meters/second =
-16 feet/second:
3) Then, use this equation to establish systems of equations with the given data:
4) Take two of these equations and subtract to get the original velocity:
-_______________________________
Meaning:
5) Lastly, plug the numbers back into the equation of your choice to establish the starting height from
the ground.
6) So, the final equation, including the original velocity and height constants, is:
NOTE: Again, this problem could be done on a calculator by going to Data/Matrices, entering the time
in seconds in c1 and the height in feet off the ground in c2, and running a Quadratic Regression
(QuadReg) on the values. Then, store the regression to y1(x) to get the graph.
Formulas and Concepts to Know From Chapter 1:
1) Midpoint Formula:
2) Distance Formula:
3) Definition of Slope:
4) Definition Of Perpendicular Line:
5) Forms of linear equations, including:
A) General Form:
B) Slope-Intercept Form:
C) Point-Slope Form:
y  y1  m( x  x1 ) OR
D) Intercept Form:
6) Complex Numbers:
Complex Numbers
a+bi
Real Numbers
b=0
e.g. 0, -7, ½, Π, etc.
Imaginary Numbers
b=0
e.g. 7i, 4-3i, i,etc.
7) Quadratic Equation:
8) Quadratic Formula:
9) Axis of Symmetry:
and the Discriminant:
NOTE: if: b 2  4ac  0 then there are two different real roots
If : b 2  4ac  0 then there are two conjugate imaginary roots
If : b 2  4ac  0 then there is one real root which is called the double root
5.