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Algebra II : Graphing Circular Inequalities

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Example Question #11 : Quadratic Inequalities

$(x+4)^2+(y+3)^2\leq4$

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

Possible Answers:

Yes

Can't tell

Maybe

Correct answer:

Yes

Explanation:

Recall the equation of circle:

(x-h)^2+(y-k)^2=r^2 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.

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Example Question #12 : Quadratic Inequalities

$(x+4)^2+(y+3)^2\leq4$

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

Possible Answers:

Inside

Both

Can't Tell

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.

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Example Question #13 : Graphing Circular Inequalities

What is the -intercept of $y = 3^{x - 3} - 9$ ?

Possible Answers:

x = 1

x = 0

x = 5

x = 3

There are no -intercepts of this function.

Correct answer:

x = 5

Explanation:

The -intercepts of a function are the points where y = 0 . When we substitute this into our equation, we get:

$0 = 3^{x - 3} - 9$ .

Adding nine to both sides,

$9 = 3^{x - 3}$ .

Modifying the equation to get like bases get us,

$3^2=3^{x-3}$

Since 9=3^2 .

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

Thus,

x - 3 = 2 .

Giving us our final solution:

x = 5 .

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Example Question #21 : Quadratic Inequalities

Which equation would produce this graph:

Circle inequality 2

Possible Answers:

(x+1)^2 + (y-5)^2 < 16

(x-1)^2 + (y-5)^2 > 16

(x-1)^2 + (y+5)^2 < 16

(x+1)^2 - (y-5)^2 > 4

(x+1)^2 + (y-5)^2 < 4

Correct answer:

(x-1)^2 + (y+5)^2 < 16

Explanation:

The general equation of a circle is (x-h)^2 + (y-k)^2 = r^2 where the center is (h,k) and the radius is .

In this case, the center is (1, -5) and the radius is , so the equation for this circle is (x-1)^2 + (y+5)^2 = 16 .

The circle is shaded on the inside, which means that choosing any point (x,y) and plugging it in for (x-1)^2 + (y+5)^2 would produce something less than .

Therefore, our answer is (x-1)^2 + (y+5)^2 < 16 .

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Example Question #22 : Quadratic Inequalities

Which equation would match to this graph:

Circle inequality 1

Possible Answers:

(x-4)^2 + y^2 > 3

1 < x^2 + y^2 < 7

x^2 + (y-4)^2 > 9

(x+4)^2 - y^2 < 9

(x-4)^2 + y^2 < 9

Correct answer:

(x-4)^2 + y^2 < 9

Explanation:

The general equation for a circle is (x-h)^2 + (y-k)^2 = r^2 where the center is (h,k) and its radius is .

In this case, the center is (4, 0) and the radius is , so the equation for the circle is (x-4)^2 + (y-0)^2 = 3^2 .

We can simplify this equation to: (x-4)^2 + y^2 = 9 .

The circle is shaded on the inside, which means that choosing any point (x,y) and plugging it in for (x-4)^2 + y^2 would produce something less than .

Therefore, our answer is (x-4)^2 + y^2 < 9 .

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Example Question #23 : Quadratic Inequalities

$(x-1)^2+(y-1)^2\geq25$

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

Possible Answers:

(7,4)

(3,3)

(0,0)

(5,2)

Correct answer:

(7,4)

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:

$(7-1)^2+(4-1)^2= 6^2+3^2=36+9\geq25$

$(5-1)^2+(2-1)^2= 4^2+1^2=16+1\leq25$

$(0-1)^2+(0-1)^2= 1^2+1^2=1+1\leq25$

$(3-1)^2+(3-1)^2= 2^2+2^2=4+4\leq25$

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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Algebra II : Graphing Circular Inequalities

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #11 : Quadratic Inequalities

Example Question #12 : Quadratic Inequalities

Example Question #13 : Graphing Circular Inequalities

Example Question #21 : Quadratic Inequalities

Example Question #22 : Quadratic Inequalities

Example Question #23 : Quadratic Inequalities

All Algebra II Resources

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