SAT II Math I : X-intercept and y-intercept

Study concepts, example questions & explanations for SAT II Math I

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Example Questions

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Example Question #1 : X Intercept And Y Intercept

Find the y-intercept of the following line.

Possible Answers:

Correct answer:

Explanation:

To find the y-intercept of any line, we must get the equation into the form

where m is the slope and b is the y-intercept.

To manipulate our equation into this form, we must solve for y. First, we must move the x term to the right side of our equation by subtracting it from both sides.

To isolate y, we now must divide each side by 3.

Now that our equation is in the desired form, our y-intercept is simply

Example Question #2 : X Intercept And Y Intercept

Solve for the -intercepts of this equation:

Round each of your answers to the nearest tenth.

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 and 

Explanation:

For an equation like this, you should use the quadratic formula to solve for the roots. We can easily get our equation into proper form by substituting  for :

Recall that the general form of the quadratic formula is:

Based on our equations, the following are your formula values:

Therefore, the quadratic formula will be:

Simplifying, you get:

Using a calculator, you will get:

 and 

Example Question #3 : X Intercept And Y Intercept

Solve for the -intercepts of this equation:

Round each of your answers to the nearest tenth.

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 and 

Explanation:

For an equation like this, you should use the quadratic formula to solve for the roots. We can easily get our equation into proper form by substituting  for :

Recall that the general form of the quadratic formula is:

Based on our equations, the following are your formula values:

Therefore, the quadratic formula will be:

Simplifying, you get:

Using a calculator, you will get:

 and 

Example Question #4 : X Intercept And Y Intercept

Solve for the -intercepts of this equation:

Round each of your answers to the nearest tenth.

Possible Answers:

 and  

 and 

 and 

 and 

 and 

Correct answer:

 and  

Explanation:

For an equation like this, you should use the quadratic formula to solve for the roots. We can easily get our equation into proper form by substituting  for . Then, we need to get it into standard form:

Recall that the general form of the quadratic formula is:

Based on our equations, the following are your formula values:

Therefore, the quadratic formula will be:

Simplifying, you get:

Using a calculator, you will get:

 and 

Example Question #5 : X Intercept And Y Intercept

What are the -intercepts of the following equation?

Round each of your answers to the nearest tenth.

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 and 

Explanation:

There are two ways to solve this. First, you could substitute in  for :

Take the square-root of both sides and get:

Therefore, your two answers are  and .

You also could have done this by noticing that the problem is a circle of radius , shifted upward by .

Example Question #6 : X Intercept And Y Intercept

Find the -intercepts of the following equation:

Round each of your answers to the nearest tenth.

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 and 

Explanation:

For an equation like this, you should use the quadratic formula to solve for the roots. We can easily get our equation into proper form by substituting  for . Then, we need to get it into standard form:

Recall that the general form of the quadratic formula is:

Based on our equations, the following are your formula values:

Therefore, the quadratic formula will be:

Simplifying, you get:

Using a calculator, you will get:

 and 

Example Question #7 : X Intercept And Y Intercept

What is the -intercept of the following equation?

Possible Answers:

None of the others

Correct answer:

Explanation:

The easiest way to solve for this kind of simple -intercept is to set  equal to .  You can then solve for the  value in order to find the relevant intercept.

Solve for :

Divide both sides by 40:

Example Question #8 : X Intercept And Y Intercept

What is the x-intercept of the above equation?

Possible Answers:

Correct answer:

Explanation:

To find the x-intercept, you must plug  in for .  

This gives you,

 and you must solve for .  

First, add  to both sides which gives you, 

.  

Then divide both sides by  to get, 

.

Example Question #9 : X Intercept And Y Intercept

Find the -intercepts of the following equation:

Round each of your answers to the nearest tenth.

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 and 

Explanation:

There are two ways to solve this. First, you could substitute in  for :

Take the square-root of both sides and get:

Therefore, your two answers are  and .

You also could have done this by noticing that the problem is a circle of radius , shifted downward by .

Example Question #10 : X Intercept And Y Intercept

What is the x-intercept of the given equation?  

Possible Answers:

Correct answer:

Explanation:

In order to determine the x-intercept, we will need to let , and solve for .

Divide both sides by two.

The answer is:  

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