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

Example Questions

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Example Question #1 : X Intercept And Y Intercept

Find the y-intercept of the following line.

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 #21 : Properties Of Functions And Graphs

Solve for the -intercepts of this equation:

and

and

and

and

and

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 #22 : Properties Of Functions And Graphs

Solve for the -intercepts of this equation:

and

and

and

and

and

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 #21 : Properties Of Functions And Graphs

Solve for the -intercepts of this equation:

and

and

and

and

and

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 #1 : X Intercept And Y Intercept

What are the -intercepts of the following equation?

and

and

and

and

and

and

Explanation:

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

Take the square-root of both sides and get:

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

Example Question #1 : X Intercept And Y Intercept

Find the -intercepts of the following equation:

and

and

and

and

and

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 #1 : X Intercept And Y Intercept

What is the -intercept of the following equation?

None of the others

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 #1 : X Intercept And Y Intercept

What is the x-intercept of the above equation?

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 #1 : X Intercept And Y Intercept

Find the -intercepts of the following equation:

and

and

and

and

and

and

Explanation:

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

Take the square-root of both sides and get:

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

Example Question #1 : X Intercept And Y Intercept

What is the x-intercept of the given equation?