Download Algebra: Quadratic Equations Test Review

9506 - 1 - Page 1
Name: ____________________________________________ Date: ___________
Algebra: Quadratic Equations Test Review
___ 1)
Find the value(s) of z in the equation
z2 + 8z + 16 = 0.
___ 2)
Find the value(s) of a in the equation
9a + 36 = a2.
___ 5)
If the square of a positive number is
decreased by five times the number, the
result is 14. Find the number.
___ 6)
For the graph of which one of the following
equations is x = 2 an equation of the axis of
symmetry?
A) 4x 2 - 2x + 10 = y
B) 3x 2 + 6x - 8 = y
C) x 2 - 4x - 6 = y
D) x 2 + 2x - 3 = y
___ 3)
Find the value(s) of x in the equation x 2 = 1.
___ 4)
Solve the given equation for all values of the
variable:
=
___ 7)
What is an equation of the axis of symmetry
of the graph whose equation is
y = x 2 + 8x - 10?
C) x = 4
A) x = -4
B) y = -4
D) y = 4
___ 8)
What is an equation of the axis of symmetry
of the parabola shown in the accompanying
graph?
___ 11)
9506 - 1 - Page 2
Which one of the following graphs could
represent the equation y = -x 2 + 4?
A)
B)
A) x = 2
B) x = -2
C) y = 2
D) y = -2
C)
___ 9)
The graph of the equation y = x 2 is a
A) parabola
B) straight line
C) point
D) circle
D)
___ 10)
Which of the following is true of the graph of
the parabola whose equation is
y = x 2 - 2x - 8?
A) The x-intercepts are at x = 4 and
x = -2.
B) The only x-intercept is at x = 4.
C) The x-intercepts are at x = 2 and
x = -4.
D) There are no x-intercepts.
___ 12)
Which one of the following equations can
___ 13)
represent the parabola in the diagram below?
A)
B)
C)
D)
9506 - 1 - Page 3
What are the coordinates of the minimum
point of a parabola whose equation is
y = x 2 + 3?
A) (-1,2)
C) (3,12)
B) (0,3)
D) (3,0)
y = -x 2 - 3
y = -x 2
y = x2
y = x2 - 3
___ 14)
Draw the graph of the equation
y = x 2 - 6x + 3 including all values of x such
that 0 < x < 6.
9506 - 1 - Page 4
___ 16)
___ 15)
(a) Draw the graph of the equation
y = x 2 - 4x - 5, including all values of x
such that -2 < x < 6.
(b) On the same set of axes, draw the graph
of the equation y = x - 5.
(c) What are the coordinates of the points
of intersection of the graphs drawn in
parts (a) and (b)?
Susan tossed a ball in the air in such a way
that the path of the ball was modeled by the
equation h = -2t 2 + 12t. In the equation, h
represents the height of the ball in feet and t
is the time in seconds.
(a) Graph h = -2t 2 + 12t for 0 < t < 6.
(b) At what time (t) is the ball at its highest
point?
c
( ) What is the maximum height of the ball?
(d) What is the height of the ball at time
t = 5?
___ 17)
What is the turning point of the parabola
whose equation is y = 2x 2 + 4x - 3?
A) (1,3)
C) (-1,-5)
B) (2,13)
D) (-2,-3)
9506 - 1 - Page 5
___ 18)
If x = 3 is the equation of the axis of
symmetry of the graph of y = x 2 - 6x + 10,
what is the y-coordinate of the turning point?
___ 19)
(a) On graph paper, sketch the graph of the
function y = x 2 - 4x + 9 in the interval
-1 < x < 5.
(b) On the same set of axes, sketch the
graph of the equation y - x = 5.
(c) Solve the following system of equations:
y = x 2 - 4x + 9
y-x=5
___ 20)
Solve the following system of equations
algebraically and check:
y = x 2 + 2x - 4
y - 5 = 2x