DIRECTIONS: Show all work on this test paper.
Solve :
Find the term that should be added to the expression to
form a perfect square trinomial . Write the
resulting perfect square trinomial in factored form.
Solve the quadratic equation by completing the square.
Rewrite the quadratic equation in the form ax2
+ bx + c = 0, then identify a, b, and c.
Use the quadratic formula to solve each problem. Leave
your answer in simplest radical form . If
the answer is not real state NR.
Solve using the quadratic formula. Use a calculator to
approximate the solution to three decimal
places.
Solve.
14) A square sheet of posterboard has an area of 169 square centimeters.
What is the length of each side? |
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Use the quadratic formula to solve each problem. Leave
your answer in simplest radical form.
15) A square sheet of paper measures 30 centimeters on each side. What
is
the length of the diagonal of this paper? |
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State the value of the discriminant and use the
discriminant to determine whether the following
equation has solutions that are: two real solutions; one real solution; or two
nonreal solutions.
Use the quadratic formula to solve each problem. Leave
your answer in simplest radical form.
Set up an equation and solve each problem.
19) Find two consecutive odd numbers such that the sum of their squares
is
74 |
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20) The length of a rectangular floor is 9 meters less than three times
the
width . If a diagonal of the rectangle is 17 meters, find the length and
width of the floor. |
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21) Find two consecutive positive integers such that the square of the
larger
integer added to four times the smaller integer is equal to 113. |
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Find the x- and y-intercepts. If no x- intercepts exist ,
state so.
Solve the equation.
Solve.
Solve the problem. Round your answer to the nearest
tenth, if necessary.
27) Two pipes together can fill a large tank in 10 hr. One of the pipes,
used
alone, takes 15 hr longer than the other to fill the tank. How long
would
each pipe take to fill the tank alone? |
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28) A man rode a bicycle for 12 mi and then hiked an additional 8 mi.
The
total time for the trip was 5 hr. If his rate when he was riding a
bicycle
was 10 mph faster than his rate walking, what was each rate? |
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Determine the direction the parabola opens, the
coordinates of the vertex and the axis of symmetry
for each of the following equations..
Graph.
Use the vertex and a few other points to sketch the
graph of the parabola . Give the equation for
the parabola's axis of symmetry.
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32) |
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Axis of symmetry____________
33) Graph the following parabola. Label the coordinates of the vertex
and
draw in the axis of symmetry. |
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