Algebra II : Quadratic Functions

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #9 : Graphing Circular Inequalities

Given the above circle inequality, which point is not on the edge of the circle?

Possible Answers:

Correct answer:

Explanation:

Recall the equation of a circle:

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

This is a graph of a circle with radius of 2 and a center of (-4,-3). The point (2,3) is not on the edge of the circle, so that is the correct answer.

All other points are exactly 2 units away from the circle's center, making them a part of the circle's edge.

Example Question #1 : Graphing Circular Inequalities

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

Possible Answers:

Correct answer:

Explanation:

The left side of the equation must be less than or equal to 4 in order to satisfy the equation, so plugging in each of the values for x and y, we see:

The only point that satisfies the inequality is the point (-3,-2), since it yields an answer that is less than or equal to 4.

Example Question #11 : Graphing Circular Inequalities

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

Possible Answers:

Yes

Maybe

Can't tell

No

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:

Outside

Can't Tell

Both

Inside

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 #13 : Graphing Circular Inequalities

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 #21 : Quadratic Inequalities

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 #22 : Quadratic 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 #23 : 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.

Example Question #1 : Graphing Hyperbolic Inequalities

Which inequality does this graph represent?
Hyp inequality 1

Possible Answers:

Correct answer:

Explanation:

The hyperbola in the question's graph is .

This could be discerned because it subtracts from and not the other way around, putting the zeros on the  axis. This narrows the answers down to and .

Test a point to tell which inequality is being used in the graph.

The point  is within the shaded region, for example. 

, which is greater than 16, so the answer is .

Example Question #2 : Graphing Hyperbolic Inequalities

Which inequality does this graph represent?
Hyp inequality 2

Possible Answers:

Correct answer:

Explanation:

The hyperbola in the graph has y-intercepts rather than x-intercepts, so the equation must be in the form and not the other way around.

The y-intercepts are at 1 and -1, so the correct equation will have just and not .

The answer not must either be,

  or .

To see which, test a point in the shaded area.

For example,

, which is less than 1, so the answer is .

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