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Hints for quadratic equation
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some
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Lesson 14:
#3: Math hint : Remember to always check for extraneous
solutions when squaring both
sides of an equation
#4, #5, #6: Math hint: After squaring both sides and
getting all terms to one side of the
equation, the resulting quadratic equation will factor by trial and error.
Remember to
always check for extraneous solutions when squaring both sides of an equation.
#7: Math hint: This equation will factor by trial and
error but you could also use the
quadratic formula. If you use the quadratic formula, remember to have:
and simplify. Then, lastly, you will need to square root
both
answers to solve the equation.
#8: Math hint: You must use the quadratic formula (or
completing the square) to solve
this equation. Again, remember to have:
and simplify. Then, lastly, you will need to square root
both
answers to solve the equation.
#9, #10, #11: These are all parts of #52 from the
textbook. Math hint: If you take an
even root of both sides of an equation, you need to include the plus/minus root.
If you
raise both sides of an equation to an even power , there is the possibility of
extraneous
solutions. Break these equations into two steps . Raise both sides first, then
take
whichever root is needed second.
#13: Math hint: The formula needed for this problem is the
surface area of a cone (given
on a quiz or exam if needed):
Leave your answer in as exact (do not round to a decimal
approximation). This is a
difficult problem. See a similar example in class.
Lesson 15
In general, you must use interval notation in the majority of answers. Always
write the
interval notation from smallest number to largest number. For example, it is not
correct
to write an interval as [7,∞)∪[3,7]. This would be counted as incorrect. It must
be
written as [3,7]∪[7,∞). This would be true in class also, not just on the
computer. Use
cup for the ∪ symbol , inf for ∞, and –inf for − ∞.
#1: Use inequalities (not interval notation).
#5: Remember to write interval notation in order from smallest number to largest number.
#6 and #7: This is a notation question, so it want the inequality (not interval notation).
#17: The absolute value tool is under the
toolbar in the bottom right corner. The
subscript tool is under the log x toolbar in the top right corner.
#18: Use the inequality for the answer (not interval notation).
#19: Use the inequality for the answer (not interval
notation). Also, use fractions and not
decimal approximations.
#20: Answer will be a number only (no inequality or interval notation needed).
Lesson 16
#4: Remember simplify the radical if possible
#7: Math hint: Use the distance formula to find the length
of each side of the triangle.
All ordered pairs are integers (no fractions are used). You can eyeball which of
the three
angles is the right angle (90 degrees). Then use A = (1/2)bh to calculate the
area . Simplify
this result (it should work out to a nice number).
#11: Math hint: Use the distance formula with two points
given and set equal to the
distance given. Square both side and solve for a. The quadratic equation WILL
factor by
trial and error. Remember which quadrant the point needed and disregard the
solution
that would be in the wrong quadrant. Calculate the coordinates with the
remaining
solution for the final answers.
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