Algebra II : Understanding Quadratic Equations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #2274 : Algebra 1

Solve for :

Possible Answers:

None of the other answers

Correct answer:

Explanation:

To solve this equation, you must first eliminate the exponent from the by taking the square root of both sides: 

Since the square root of 36 could be either or , there must be 2 values of . So, solve for

and

to get solutions of .

Example Question #1 : Quadratic Roots

Find the roots of 

Possible Answers:

Correct answer:

Explanation:

When we factor, we are looking for two number that multiply to the constant, , and add to the middle term, . Looking through the factors of , we can find those factors to be  and .

Thus, we have the factors: 

.

To solve for the solutions, set each of these factors equal to zero.

Thus, we get , or .

Our second solution is, , or 

Example Question #1451 : Algebra Ii

Write a quadratic function in standard form with roots of -1 and 2.

Possible Answers:

Correct answer:

Explanation:

From the zeroes we know

Use FOIL method to obtain:

Example Question #1453 : Algebra Ii

Select the quadratic equation that has these roots: 

Possible Answers:

None of these.

Correct answer:

Explanation:

FOIL the two factors to find the quadratic equation.

First terms:

Outer terms:

Inner terms:

Last terms:

Simplify:

Example Question #1454 : Algebra Ii

Solve for a possible root:   

Possible Answers:

Correct answer:

Explanation:

Write the quadratic equation.

The equation  is in the form .

Substitute the proper coefficients into the quadratic equation.

The negative square root can be replaced by the imaginary term .  Simplify square root 60 by common factors of numbers with perfect squares.

Simplify the fraction.

A possible root is:   

Example Question #1455 : Algebra Ii

Solve for the roots (if any) of  

Possible Answers:

Correct answer:

Explanation:

Pull out a common factor of negative four.

The term inside the parentheses can be factored.

Set the binomials equal to zero and solve for the roots.  We can ignore the negative four coefficient.

The answers are:  

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