Algebra II : Quadratic Formula

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #141 : Functions And Lines

Which of the following is the correct solution when    is solved using the quadratic equation?

Possible Answers:

Correct answer:

Explanation:

Example Question #21 : Quadratic Formula

Solve the equation using the quadratic formula.

Possible Answers:

Correct answer:

Explanation:

The quadratic formula is

.

Setting , ,  yields,

 

Example Question #21 : Quadratic Formula

Find the roots of:  

Possible Answers:

Since the quadratic cannot be factored, there are no roots.

Correct answer:

Explanation:

Identify the values of , and  in the standard form of the parabola.

Calculate the discriminant.

Since the discriminant is less than zero, the quadratic is irreducible and there are no real roots. However, there are complex roots.  Use the quadratic formula to determine the complex roots.

Example Question #24 : Quadratic Formula

Use the quadratic formula to find the roots of .

Possible Answers:

 and 

 and 

 and 

no solution

Correct answer:

 and 

Explanation:

The parent function of a quadratic is represented as . The quadratic formula is . In this case , and . Replacing these values into the quadratic forumula will give you the solutions to the quadratic. 

 and 

Example Question #491 : Intermediate Single Variable Algebra

Solve this quadratic equation by using the quadratic formula: 

Possible Answers:

Correct answer:

Explanation:

You must know the quadratic equation .

To plug in the right terms, recognize that polynomials in standard form are symbolized as .

Plug in the values from your equation

simplify within the radical:

Simplify the radical:

Reduce:

 

Note that this represents two values since there is a  in the equation. One is solved with an addition sign and the other is solved with a subtraction sign to yield two answers or roots where this equation crosses the x axis. 

 

Example Question #82 : Systems Of Equations

Solve for .

Possible Answers:

Correct answer:

Explanation:

1) Begin the problem by factoring the final term. Include the negative when factoring.

–2 + 2 = 0

–4 + 1 = –3

–1 + 4 = 3

All options are exhausted, therefore the problem cannot be solved by factoring, which means that the roots either do not exist or are not rational numbers. We must use the quadratic formula.

 

Example Question #23 : Quadratic Formula

Solve the quadratic equation:

Possible Answers:

Correct answer:

Explanation:

The standard form of a quadratic equation is , where a,b, and c are constants. Plug these constants into the quadratic formula to solve for x.

Example Question #24 : Quadratic Formula

Solve for  by using the quadratic formula:

Possible Answers:

None of the above

Correct answer:

Explanation:

The quadratic equations is:

From here you just plug in your numbers, so:

Simplify:

Then you need to simplify the inside looking for perfect squares:

Each term is divisible by 2, so your final answer is:

Example Question #25 : Quadratic Formula

Use the quadratic formula to solve the equation 

Possible Answers:

Correct answer:

Explanation:

Example Question #26 : Quadratic Formula

Find the zeros of ?

Possible Answers:

Correct answer:

Explanation:

This specific function cannot be factored, so use the quadratic equation:

Our function is in the form  where, 

Therefore the quadratic equation becomes,

 

 OR 

 OR 

  OR  

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