1. Chapter 1 Review
Functions and Their Graphs

2. tutorial review, try the links
The material in chapter 1 has
been covered in your previous
math courses. A summary is
listed on p.48. If you need more
tutorial review, try the links at
Check the Precal PPTS.

3. (x1,y1) y1 y2 c2 d a2
ly2-y1l
(x2,y2) b2
lx2-x1l
x x2

4. Distance formula is based
on Pythagorean Theorem. √
c =
a b2

5. (5, 1) and ( 2, -6 ) (x1, y1) (x2, y2) ( 2 - 5)2 + ( -6 - 1 )2
1a Find distance between
(5, 1) and ( 2, -6 )
(x1, y1)
(x2, y2)
( 2 - 5)2 + ( )2

6. careful ! this is not - 32 ( 2 - 5)2 + ( -6 - 1 )2 d = √
(- 3) ( - 7 )2 58
careful !
this is not
- 32
d = √
d = √
= 7.6

7. (-3)2 = 9
-32 is NOT the same
Don’t forget
the ( ) !!!

8. and (x2, y2) the midpoint is
1b) For any 2 points (x1, y1)
and (x2, y2) the midpoint is
(x1,y1)
(x2,y2)

9. m = 12 - 4 = 8 13 - 9 = 2 4 m = y2 - y1 x2 - x1 Find m (9, 4) (13, 12)1c
m = y2 - y1
x2 - x1
Slope
Find m (9, 4) (13, 12)
m =
13 - 9
= 8 4
= 2

10. vertical line through (2, 4 ).
1d) Find an equation for a
vertical line through (2, 4 ).
2) Vertical line
has undefined
slope.
X = 2

11. Same slope. m = 2 3) y1 = 2 x + 1 y2 = 2 x - 3
Why are the lines parallel ?
Same slope.
m = 2
y1 = 2 x + 1
y2 = 2 x - 3

12. 3 Perpendicular Lines y = 3/4 X + 2 y = - 4/3 X slopes have
On your
calculator
use ( ) on
fractions
slopes have
opposite signs
& are reciprocals
y= -4/3 x
 lines

13. General or Standard Ax + By = C Slope Intercept y = mx + b4)
Forms of Linear Equations
General or Standard
Ax + By = C
Slope Intercept
y = mx + b

14. Forms of Linear Equations
Point Slope Form
y - y1
x - x1
=m or y -y1= m(x - x1) x a y b =1 +
Intercept Form

15. 5)
Function - for each X
there is only one Y.
Zero of the function is
where the graph
crosses the
X axis.

16. √ i 2 = -1 and √-1 = i 6a) Imaginary Numbers no answer in Reals - 9
Define
i 2 = and √-1 = i

17. a + bi (a and b are reals. i is imaginary)
6b Form of a complex number
a + bi (a and b are reals. i is imaginary)
The conjugate is a - bi .
( a + bi ) (a - bi ) =
a2 - (bi )2 =
a2 - b2 (-1) =
a2 + b2

18. Reals and imaginary numbers
are subsets of
COMPLEX NUMBERS.

19. 7
Solving Quadratics
Ax2 + Bx + C = Y

20. Quadratics
Solve by factoring.
x2 - 4 = 0
(x+2)(x-2) = 0
x+2 = 0 or x - 2 = 0
x = x = 2

21. substituting negatives
Solve with Quadratic Formula
4 x2 – 8 x + 1 = 0
a b c
Careful when
substituting negatives

22. x= 8
x = 8
x = 8 or
=1.86
=.14

23. x2 + 6x -7 = 0 +7 +7 x2 + 6x = 7 Solve by completing the square.
x2 + 6x = 7
1) Be sure the coefficient of
the x2 term is 1.
2) Get the constant on the other side.

24. Solve by completing the square.
x2 + 6x -7 = 0
x2 + 6x = 7
6 / 2 =3
32 = 9
x2 + 6x +9 = 7+9
3)Take half the coefficient of
the x term .Square it.
Add to both sides.

25. x2 + 6x -7 = 0 x2 + 6x = 7 x2 + 6x +9 = 7+9 (x + 3)2 = 16
Solve by completing the square.
x2 + 6x -7 = 0
x2 + 6x = 7
x2 + 6x +9 = 7+9
(x + 3)2 = 16
4) Factor the left.
Simplify the right.

26. x2 + 6x -7 = 0 x2 + 6x = 7 x2 + 6x +9 = 7+9 (x + 3)2 = 16
Solve by completing the square.
x2 + 6x -7 = 0
x2 + 6x = 7
x2 + 6x +9 = 7+9
(x + 3)2 = 16
√ √
(x + 3 ) = +4
5) Take the square root both sides.

27. x2 + 6x -7 = 0 x2 + 6x = 7 x2 + 6x +9 = 7+9 (x + 3)2 = 16
Solve by completing the square.
x2 + 6x -7 = 0
x2 + 6x = 7
x2 + 6x +9 = 7+9
(x + 3)2 = 16
√ √
(x + 3 ) = +4
x+3 = 4 or x +3 = -4
6)Solve

28. x2 + 6x -7 = 0 x2 + 6x = 7 x2 + 6x +9 = 7+9 (x + 3)2 = 16
Solve by completing the square.
x2 + 6x -7 = 0
x2 + 6x = 7
x2 + 6x +9 = 7+9
(x + 3)2 = 16
√ √
(x + 3 ) = +4
x = 1 or x = -7
6)Solve

29. Quadratics
Solve with a graph.
X2- 4 = 0
(-2,0)
(2,0)
graph
X2- 4 = Y

30. Y = Ax2 + Bx + C
Y = 2x2 - 4x - 1
Vertex (-b/2a, ) -b 2a
-(-4)
2(2) =
= 1

31. Y = Ax2 + Bx + C
Y = 2x2 - 4x - 1
Vertex (-b/2a, )
( 1 , )
substitute
(1, -3)

32. Y = Ax2 + Bx + C
Y = 2x2 - 4x - 1
vertex (1, -3)
line of symmetry
X = 1

33. Vertex Form
y = a(x -h)2 + k
y = 2(x -1)2 - 2
vertex (h, k )

34. thought for the day
Mistakes are
the portals
of discovery.