CHAPTER 1
TEST REVIEW
#4 pg 5
What is the length and midpoint of line
“CD”? Coordinates: C(-2,-1); D(4,9)
A) Length:
a) Use the distance formula:
b) Insert the points
c) Calculate
=
d) Simplify
=
X
=
#4 pg 5, cont.
What is the length and midpoint of line
“CD”? Coordinates: C(-2,-1); D(4,9)
B) Midpoint:
a) Use the midpoint formula:
b) Insert the points
c) Calculate
d) Simplify
(1,4)
Example pg.2
Solve the equations simultaneously to find the intersection
point. Graph and label the intersection point.
A) Solve the equations: 2x + 5y = 10, and 3x + 4y = 12
a) Multiply in order to make a common factor
(x3)
(x2)
2x + 5y = 10
3x + 4y = 12
=
=
6x + 15y = 30
6x + 8y = 24
b) Now subtract the bottom equation from the
top to yield:
7y = 6
c) Divide both sides by 7:
y = 6/7
d) Plug y back in to solve for x:
2x + 5(6/7) = 10
x = 20/7
#9 pg.5
Given: 3x - ay = 15, find a if (9, 6) lies
on this line.
A) Plug in x and y. 3(9) - a(6) = 15
B) Solve for a. a = 2.
#13 pg.11
Find the slope and the y intercept of
the following equation: 4x – 2y = 8
a) Rearrange the equation into the
slope intercept form.
b) subtract 4x: -2y = -4x + 8
c) divide by -2: y = 2x – 4
d) the slope is 2, the y intercept is -4
#18 pg.11
Which of the following equations have
parallel lines and which have
perpendicular?
a) 3y = 5x - 5
b) y = -3x/5 +4
c) 10y = -6x -7
d) parallel lines: b and c, perpendicular
lines: a and b, a and c,
#6 pg.16
Write the equation of the line that
passes through the points (0,5) and
(6,1).
a) First you must find the slope, using the slope
equation
b) Plugging in your numbers you get the slope to be 2/3
c) Plug in one of the points into the equation
y = mx + b to find the y intercept
d) 1 = (-2/3) (6) + b, b = 5
e) The equation: y = -2x/3 + 5
#13
Find the equation of the line that passes
through the point (8, -2) and is
perpendicular to the line y =-2x + 7
a) The slope is the negative reciprocal of -2,
so it is ½.
b) Plug in the point to solve for b.
c) -2 = (1/2) (8) + b, b = -6.
d) The equation is y = x/2 – 6
#5
Find the equation of the line that passes
through the points (8, 3) and (2, -1)
a) Using the slope formula, we get the slope
to be 2/3
b) Now plug in a point to solve for b
c) 3 = (2/3) (8) + b, b = -7/3
d) The equation is y = 2x/3 – 7/3
#4
Find the equation of the line that has an x
intercept of -1 and a y intercept of 6.
a) Since these are our intercepts, we know our
two points are (-1, 0) and (0, 6).
b) Once again, using the slope formula, the slope
is 6.
c) Plug in one of your points: 6 = 6(0) + b, b = 6.
d) The equation is y = 6x + 6
#7
Find the equation of the horizontal line that passes
through the point (5, -7)
a) This is a horizontal line, meaning it has a
slope of 0
b) Every y coordinate on this line will be -7, so
that is also the y intercept.
c) The equation is y = -7.
#12
Find the equation of the line that
passes through the point (-2, 4) and
parallel to the line that passes
through the points (1, 1) and (5, 7)
a) First we must find the slope of the line
through (1, 1) and (5, 7) using the slope
equation
b) This gives us a slope of 3/2, now plug
in (-2, 4) to solve for b.
c) 4 = (3/2) (-2) + b, b = 7
d) The equation is y = 3x/2 + 7
#16 pg. 23
A recording studio invests $24,000 to
produce a master tape of a singing group. It
costs $1.50 to make each copy of the
master and cover the operating costs
a) Express the cost of producing t tapes
as a function C(t).
b) C(t) = 1.5t + 24,000
c) If each tape is sold for $6.50, express the
revenue (the total amount received from the sale)
as a function R(t).
d) R(t) = 6.5t
#2 pg. 28
Simplify: √-49 - √-9 + √-36)
a) 7i – 3i + 6i = 10i
#4 pg. 28
Simplify: √-2 x √-5
a) - √10
#11 pg. 28
Simplify (6-i)(6+i)
a) Using FOIL method, you get
36 + 6i -6i – i2
b i2 = -1, so the answer is 37
#21 pg. 28
Simplify (5+i)/(5-i)
a) answer:
12/13 + 5i/13
Solve for x or y:
a) (2x – 1)2 = -4
b) Take the square root of both sides:
2x – 1 = (+ or -) 2i
c) Add one: 2x = 1 (+ or -) 2i
d) Divide by two: x = ½ (+ or -) i
e) y2 – 8y = 2
f) y = 4 (+ or –) 3 √2
y= 4 3
Example 1 pg. 38
Sketch the parabola y=2x2 -8x + 5.
Label the x intercepts, the axis of
symmetry, and vertex.
a) Find the intersection points with the
line y = 2x + 5
b) Answer:
(0,5)
y= 4 3
Finding a Quadratic
Equation
C(x) = ax2 + bx + c
a) Given that C(12)= 152, C(22)=105, and
C(30) = 165, set up the three equations to
solve for a, b, and c
152 = a(12²) + b(12) + c
y= 4 3
105 = a(22²) + b(22) + c
165 = a(30²) + b(30) + c
Solve the equations simultaneously to find
the quadratic equation.