This page contains peer generated solutions and error explanations to OFSA questions. As you read or view the solutions, be critical: check for accuracy, but also for more efficient solution strategies. If you have a better method or different idea/answer, post a discussion and monitor the responses.

Quick Directions

Post answers, solutions and error explanations to each OFSA question below.

For each "distractor" or incorrect answer choice, explain the error that would lead to that incorrect answer choice.

You may either do the above in typed format or using a pencast.

Separate each question with a section bar.

After each solution, provide a hyperlink back to the corresponding OFSA page.

Error Explanation 1
A is not correct, because the left side of the graph is showing, which means it must be an x= equation, and negative. This also rules out D as an answer.
B is not correct because the shifts are reversed, meaning the number outside the radical is now the horizontal shift, and the number inside the parenthesis with the y is now the vertical shift.
Click here to return to OFSA. Question 2 What is the equation for this graph?:

A:

B:

C:

D:

Solution 2
A:

Error Explanation 2
Inside each hyperbola is an imaginary ellipse with a horizontal radius (in which this case shows how far apart the parts of the hyperbola are) and a vertical radius (which is only used to find the slope of the asymptote).
B is not correct because the fraction in front of the radical is the horizontal radius over the vertical radius, as well as the slope of the asymptote. It is flipped in B.
C is not correct, because the number under the radical,

is the horizontal radius of the graph, not the vertical radius.
D is not correct, because the format described graphs a vertical hyperbola, and the graph shown is a horizontal hyperbola.
Click here to return to OFSA. Question 3 The Parametric equation:

is equal to which equation?
x=4csc(t), y= 2cot(t), 0
A:

B:

C:

D:

Solution 3
The solution is
C:

When graphed as their components, the two parts of the parametrics form the graphs:

and:

When graphed as a full parametric, they form the graph:

Error Explanation 3
A is wrong because the slope is reversed for the asymptotes of the parabola.
B is wrong because it forms an ellipse rather than a hyperbola.
D is wrong because it forms a vertical hyperbola, rather than a horizontal one.
Click here to return to OFSA. Question 4 What type of graph does this equation make:

A: Right half of an ellipse
B: Top half of a hyperbola
C: Bottom half of an ellipse
D: Bottom half of a circle

Solution 4
C: Bottom half of an ellipse

Error Explanation 4
A is incorrect because it's a y= equation
B is incorrect because when x^2 is added to the other side, it forms the equation of an Ellipse and NOT a hyperbola
D is incorrect because there is a fraction before the radical in the equation, which tells us that it's not the equation of a cirlce
Click here to return to OFSA. Question 5 What is the number in front of the radical for the equation of this graph?

A: 1
B: 1/3
C: 5/4
D: 1/2

Solution 5
B: 1/3 Error Explanation 5
A is incorrect because a 1 in front of the radical would make a circle graph
C and D are incorrect because they are not the correct slope of the graph's asymptotes

Click here to return to OFSA. Question 6 Which direction does the graph of this equation open up, and what portion of the graph is used?

A: Opens North-South, and uses right portion
B: Opens East-West, and uses left portion
C: Opens North-South, and uses bottom portion
D: Opens East-West, and uses top portion

Solution 6
D: Opens East-West, and uses top portion
because it would seem like the graph opens North-South, but because of the -25, it actually opens East-West and then the positive fraction before the radical tells us to use the top (positive) part of the graph

Error Explanation 6
A is incorrect because it would only use the right portion if the fraction before the radical was positive, and it was an x= equation
B is incorrect because it would only use the left portion if the fraction before the radical was negative
C is incorrect because it would only open North-South if the -25 was +25, and it would only use the bottom portion if the fraction before the radical was negative

Click here to return to OFSA. Question 7 What type of conic created by the following equation?

A.) The top half of a parabola
B.) The bottom half of a parabola
C.) The left half of a parabola
D.) The right half of a parabola

Solution 7
The answer is A.

Error Explanation 7
B.) This answer is incorrect because of the lack of a negative sign outside of the radical, if there was a negative sign, then the bottom values would be included.
C.) This answer is incorrect because the parabola opens left-right, not top-down.
D.) This answer is incorrect because the parabola opens left-right, not top-down.

Click here to return to OFSA. Question 8 Which of the following is the equation of an ellipse?

A.)

B.)

C.)

D.)

Solution 8
The correct answer is C.

Error Explanation 8
A.) This answer is incorrect because this is an equation of a hyperbola.
B.) This answer is incorrect because this is an equation of a parabola.
D.) This answer is incorrect because this is an equation of a circle.

Click here to return to OFSA. Question 9 How does vertical shifting of a hyperbola get affected in the following equation?

A.) a
B.) b
C.) c
D.) d

Solution 9
The answer is D.

Error Explanation 9
A.) This answer is incorrect because a represents the length of the horizontal axis.
B.) This answer is incorrect because b represents the length of the vertical axis.
C.) This answer is incorrect because c represents the horizontal shift.

Click here to return to OFSA. Question 10 What type of graph does this equation make? y=3sqrt(4+x^2)

A.) Bottom half of ellipse
B.) Right half of ellipse
C.) Top half of Hyperbola
D.) Right half of Hyperbola

Solution 10
C.) Error Explanation 10
A.) The 3 in the front is not negative, so it cannot be the bottom half (negative y values), and it needs to be minus x^2 for an ellipse.
B.) If x and y switched places and it was a minus y^2
D.) If x and y switched places
Click here to return to OFSA. Question 11 What is the slope of the asymptotes in the graph from problem 10, If they exist?
A.) 2/9
B.) 9/2
C.) 9
D.) do not exist Solution 11
B.) Error Explanation 11
A.) This is the x value over the y value
C.) the x value of the rectangle goes out by 2, not 1
D.) It is a hyperbola, so it must have asymptotes
Click here to return to OFSA. Question 12 Solution 12 Error Explanation 12
Click here to return to OFSA. Question 13 Solution 13 Error Explanation 13
Click here to return to OFSA. Question 14 Solution 14 Error Explanation 14
Click here to return to OFSA. Question 15 Solution 15 Error Explanation 15
Click here to return to OFSA. Question 16 Solution 16 Error Explanation 16
Click here to return to OFSA. Question 17 Solution 17 Error Explanation 17
Click here to return to OFSA. Question 18 Solution 18 Error Explanation 18
Click here to return to OFSA. Question 19 Solution 19 Error Explanation 19
Click here to return to OFSA. Question 20 Solution 20 Error Explanation 20
Click here to return to OFSA. Question 21 Solution 21 Error Explanation 21
Click here to return to OFSA. Question 22 Solution 22 Error Explanation 22
Click here to return to OFSA. Question 23 Solution 23 Error Explanation 23
Click here to return to OFSA. Question 24 Solution 24 Error Explanation 24
Click here to return to OFSA.

This page contains peer generated solutions and error explanations to OFSA questions. As you read or view the solutions, be critical: check for accuracy, but also for more efficient solution strategies. If you have a better method or different idea/answer, post a discussion and monitor the responses.

Quick DirectionsQuestion 1What is the equation for this graph?:A:

B:

C:

D:

Solution 1C:

Error Explanation 1A is not correct, because the left side of the graph is showing, which means it must be an x= equation, and negative. This also rules out D as an answer.

B is not correct because the shifts are reversed, meaning the number outside the radical is now the horizontal shift, and the number inside the parenthesis with the y is now the vertical shift.

Click here to return to OFSA.

Question 2What is the equation for this graph?:A:

B:

C:

D:

Solution 2A:

Error Explanation 2Inside each hyperbola is an imaginary ellipse with a horizontal radius (in which this case shows how far apart the parts of the hyperbola are) and a vertical radius (which is only used to find the slope of the asymptote).

B is not correct because the fraction in front of the radical is the horizontal radius over the vertical radius, as well as the slope of the asymptote. It is flipped in B.

C is not correct, because the number under the radical,

is the horizontal radius of the graph, not the vertical radius.

D is not correct, because the format described graphs a vertical hyperbola, and the graph shown is a horizontal hyperbola.

Click here to return to OFSA.

Question 3The Parametric equation:is equal to which equation?x=4csc(t), y= 2cot(t), 0

A:

B:

C:

D:

Solution 3The solution is

C:

When graphed as their components, the two parts of the parametrics form the graphs:

and:

When graphed as a full parametric, they form the graph:

Error Explanation 3A is wrong because the slope is reversed for the asymptotes of the parabola.

B is wrong because it forms an ellipse rather than a hyperbola.

D is wrong because it forms a vertical hyperbola, rather than a horizontal one.

Click here to return to OFSA.

Question 4What type of graph does this equation make:A: Right half of an ellipse

B: Top half of a hyperbola

C: Bottom half of an ellipse

D: Bottom half of a circle

Solution 4C: Bottom half of an ellipse

Error Explanation 4A is incorrect because it's a y= equation

B is incorrect because when x^2 is added to the other side, it forms the equation of an Ellipse and NOT a hyperbola

D is incorrect because there is a fraction before the radical in the equation, which tells us that it's not the equation of a cirlce

Click here to return to OFSA.

Question 5What is the number in front of the radical for the equation of this graph?A: 1

B: 1/3

C: 5/4

D: 1/2

Solution 5B: 1/3

Error Explanation 5A is incorrect because a 1 in front of the radical would make a circle graph

C and D are incorrect because they are not the correct slope of the graph's asymptotes

Click here to return to OFSA.

Question 6Which direction does the graph of this equation open up, and what portion of the graph is used?A: Opens North-South, and uses right portion

B: Opens East-West, and uses left portion

C: Opens North-South, and uses bottom portion

D: Opens East-West, and uses top portion

Solution 6D: Opens East-West, and uses top portion

because it would seem like the graph opens North-South, but because of the -25, it actually opens East-West and then the positive fraction before the radical tells us to use the top (positive) part of the graph

Error Explanation 6A is incorrect because it would only use the right portion if the fraction before the radical was positive, and it was an x= equation

B is incorrect because it would only use the left portion if the fraction before the radical was negative

C is incorrect because it would only open North-South if the -25 was +25, and it would only use the bottom portion if the fraction before the radical was negative

Click here to return to OFSA.

Question 7What type of conic created by the following equation?A.) The top half of a parabola

B.) The bottom half of a parabola

C.) The left half of a parabola

D.) The right half of a parabola

Solution 7The answer is A.

Error Explanation 7B.) This answer is incorrect because of the lack of a negative sign outside of the radical, if there was a negative sign, then the bottom values would be included.

C.) This answer is incorrect because the parabola opens left-right, not top-down.

D.) This answer is incorrect because the parabola opens left-right, not top-down.

Click here to return to OFSA.

Question 8Which of the following is the equation of an ellipse?A.)

B.)

C.)

D.)

Solution 8The correct answer is C.

Error Explanation 8A.) This answer is incorrect because this is an equation of a hyperbola.

B.) This answer is incorrect because this is an equation of a parabola.

D.) This answer is incorrect because this is an equation of a circle.

Click here to return to OFSA.

Question 9How does vertical shifting of a hyperbola get affected in the following equation?A.) a

B.) b

C.) c

D.) d

Solution 9The answer is D.

Error Explanation 9A.) This answer is incorrect because a represents the length of the horizontal axis.

B.) This answer is incorrect because b represents the length of the vertical axis.

C.) This answer is incorrect because c represents the horizontal shift.

Click here to return to OFSA.

Question 10What type of graph does this equation make?y=3sqrt(4+x^2)A.) Bottom half of ellipse

B.) Right half of ellipse

C.) Top half of Hyperbola

D.) Right half of Hyperbola

Solution 10C.)

Error Explanation 10A.) The 3 in the front is not negative, so it cannot be the bottom half (negative y values), and it needs to be minus x^2 for an ellipse.

B.) If x and y switched places and it was a minus y^2

D.) If x and y switched places

Click here to return to OFSA.

Question 11What is the slope of the asymptotes in the graph from problem 10, If they exist?A.) 2/9

B.) 9/2

C.) 9

D.) do not exist

Solution 11B.)

Error Explanation 11A.) This is the x value over the y value

C.) the x value of the rectangle goes out by 2, not 1

D.) It is a hyperbola, so it must have asymptotes

Click here to return to OFSA.

Question 12Solution 12Error Explanation 12Click here to return to OFSA.

Question 13Solution 13Error Explanation 13Click here to return to OFSA.

Question 14Solution 14Error Explanation 14Click here to return to OFSA.

Question 15Solution 15Error Explanation 15Click here to return to OFSA.

Question 16Solution 16Error Explanation 16Click here to return to OFSA.

Question 17Solution 17Error Explanation 17Click here to return to OFSA.

Question 18Solution 18Error Explanation 18Click here to return to OFSA.

Question 19Solution 19Error Explanation 19Click here to return to OFSA.

Question 20Solution 20Error Explanation 20Click here to return to OFSA.

Question 21Solution 21Error Explanation 21Click here to return to OFSA.

Question 22Solution 22Error Explanation 22Click here to return to OFSA.

Question 23Solution 23Error Explanation 23Click here to return to OFSA.

Question 24Solution 24Error Explanation 24Click here to return to OFSA.