Algebra II : Graphing Circular Inequalities

Study concepts, example questions & explanations for Algebra II

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Example Questions

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Example Question #11 : Graphing Circular Inequalities

Given the above circle inequality, does the center satisfy the equation?

Possible Answers:

Yes

No

Can't tell

Maybe

Correct answer:

Yes

Explanation:

Recall the equation of circle:

 where r is the radius and the center of the circle is at (h,k).

The center of the circle is (-4,-3), so plugging those values in for x and y yields the response that 0 is less than or equal to 4, which is a true statement, so the center does satisfy the inequality. 

Example Question #12 : Graphing Circular Inequalities

Given the above circle inequality, is the shading on the graph inside or outside the circle?

Possible Answers:

Inside

Can't Tell

Both

Outside

Correct answer:

Inside

Explanation:

Check the center of the circle to see if that point satisfies the inequality. When evaluating the function at the center (-4,-3), we see that it does satisfy the equation, so it can be in the shaded region of the graph. Therefore the shading is inside of the circle.

Example Question #1041 : Algebra Ii

What is the -intercept of 

Possible Answers:

There are no -intercepts of this function. 

Correct answer:

Explanation:

The -intercepts of a function are the points where . When we substitute this into our equation, we get: 

Adding nine to both sides, 

Modifying the equation to get like bases get us,

Since .

Now we can set the exponents equal to eachother and solve for .

Thus, 

Giving us our final solution: 

Example Question #124 : Quadratic Functions

Which equation would produce this graph:

Circle inequality 2

Possible Answers:

Correct answer:

Explanation:

The general equation of a circle is where the center is and the radius is .

In this case, the center is and the radius is , so the equation for this circle is .

The circle is shaded on the inside, which means that choosing any point  and plugging it in for would produce something less than .

Therefore, our answer is .

Example Question #13 : Graphing Circular Inequalities

Which equation would match to this graph:

Circle inequality 1

Possible Answers:

Correct answer:

Explanation:

The general equation for a circle is where the center is and its radius is .

In this case, the center is  and the radius is , so the equation for the circle is .

We can simplify this equation to: .

The circle is shaded on the inside, which means that choosing any point and plugging it in for  would produce something less than

Therefore, our answer is .

Example Question #21 : Quadratic Inequalities

Given the above circle inequality, which point satisfies the inequality?

Possible Answers:

Correct answer:

Explanation:

The left side of the equation must be greater than or equal to 25 in order to satisfy the equation, so plugging in each of the values for x and y, we see that:

The only point that satisfies the inequality is (7,4) since it yields an answer that is greater than or equal to 25.

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