Algebra II : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #122 : Understanding Quadratic Equations

Evaluate the discriminant, if any:  

Possible Answers:

Correct answer:

Explanation:

The formula to determine the discriminant is:  

To determine the discriminant, we will need to put the equation in standard form:

Add  on both sides.

Subtract  on both sides.

Reorder the terms on the left.

Divide by two on both sides.

The equation in standard form is: 

The coefficients can be determined to calculate the discriminant.

Substitute the values into the formula.

The answer is:  

Example Question #31 : Discriminants

Determine the discriminant:  

Possible Answers:

  

Correct answer:

  

Explanation:

The formula for the discriminant is: 

Given the polynomial in standard format, we can identify the coefficients of the polynomial to substitute into the equation.

Substitute all the numbers into the equation.

The answer is: 

Example Question #31 : Discriminants

Evaluate the discriminant:  

Possible Answers:

Correct answer:

Explanation:

Write the formula for the discriminant.  The discriminant is the term inside the square root of the quadratic formula.

Determine the coefficients.

Substitute the terms into the formula.

The answer is:  

Example Question #131 : Understanding Quadratic Equations

What is the discriminant?  

Possible Answers:

Correct answer:

Explanation:

The equation is already in the standard form of , where the discriminant is defined as: 

Following the coefficients of each term with the polynomial in standard form, we can determine the values of each variable.

Substitute the terms into the equation.

The answer is:  

Example Question #132 : Understanding Quadratic Equations

Identify the discriminant of the parabola given the roots:  

Possible Answers:

Correct answer:

Explanation:

We will need to use the roots to write the quadratic equation.

Simplify by using the FOIL method.

The discriminant of the parabola in standard form is defined as:  

where .

Substitute the values in the equation.

The answer is:  

Example Question #1434 : Algebra Ii

Evaluate the discriminant:  

Possible Answers:

Correct answer:

Explanation:

The given equation is not fully simplified in standard form:   

Distribute the negative three across each term in the parentheses.

Write the formula for the discriminant.

Substitute the known terms.

The answer is:  

Example Question #133 : Understanding Quadratic Equations

Identify the discriminant:  

Possible Answers:

Correct answer:

Explanation:

The equation is already in standard form .

Following the coefficients: 

The discriminant is the term inside the square root of the quadratic equation.

Substitute the values.

The discriminant is:  

Example Question #1436 : Algebra Ii

Determine the discriminant if the parabola has  as roots.

Possible Answers:

Correct answer:

Explanation:

Given the roots, we can set up the binomials of the parabola.

Use the FOIL method to simplify these binomials.

Simplify all the terms by distribution.

The equation of the parabola in standard form is: 

The equation of the discriminant is the square root of the term under the radical of the quadratic equation.  Substitute the terms into the equation.

The answer is:  

Example Question #134 : Understanding Quadratic Equations

Determine the discriminant of the parabola:  

Possible Answers:

Correct answer:

Explanation:

Write the formula for the discriminant.  This is the term inside the radical of the quadratic equation.

Substitute the values into the equation.

The answer is:  

Example Question #135 : Understanding Quadratic Equations

Determine the discriminant of the following function:  

Possible Answers:

Correct answer:

Explanation:

The equation is already in standard form:  

Identify the coefficients.

The formula for the discriminant is:

Substitute the values into the equation.

The answer is:  

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