(1) Solve each equation. Check for extraneous solutions.
(a)
(b) √
(d)
(e)
|
(c)
(
|
(f) √
)
(2) Solve the system of equations:
(3) Write an equation of the form
that passes through the points (0,—1), (2,23) and (3,50).
( )
)
,
( )
PROVE IT:
(b) Which functions have exactly
one real root?
PROVE IT:
(a) Which functions have
zero real roots?
(
,
( )
and
( )
(
) .
(c) Which functions have two
real roots?
PROVE IT:
(4) Consider the functions
(5) Circle all of the following phrases that describe the translation of the graph of
(
)
graph of
.
UP 3
LEFT 7
VERTICALLY STRETCHED
FACES UPWARDS
DOWN 3
RIGHT 7
VERTICALLY COMPRESSED
FACES DOWNWARDS
(
)
to the
y
(6) Graph the parabola formed by the equation
X-INTERCEPTS:
.
Y-INTERCEPT:
VERTEX:
DOMAIN:
x
GRAPHING
FORM:
RANGE:
(7) Write each equation in graphing form. State the coordinates of its vertex.
(a)
(b)
GRAPHING
FORM:
GRAPHING
FORM:
VERTEX:
VERTEX:
(8) Consider the graph of a parabola with a vertex of (—5,—1) that passes through the point (—3,—13).
(a) Calculate the a-value of the parabola.
(b) Write the equation of the parabola.
(9) The University of Arkansas wants to construct a balloon arch for its football team to run through
prior to each game. They have designed an arch shaped like a rounded capital letter “A.” The curved
part of the “A” shape can be modeled by the equation
. The crossbar of the
“A” shape can be modeled by the equation
. All measurements are given in feet.
(a) Draw an accurate graph of the “A” shaped arch,
including the crossbar. Label all important points.
(b) Write the equation of
the “A” shaped arch in
graphing form.
(c) What is the vertical distance from the
crossbar to the highest point of the arch?
(d) From end to end, how long is the crossbar?