Common Core: High School - Algebra : Solve Quadratic Equations by Inspection, Quadratic Formula, Factoring, Completing the Square, and Taking Square Roots: CCSS.Math.Content.HSA-REI.B.4b

Study concepts, example questions & explanations for Common Core: High School - Algebra

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Example Questions

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Example Question #1 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve 

Possible Answers:

Correct answer:

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

, , and  correspond to coefficients in the quadratic equation, which is

In this case , and  .

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an , outside the square root sign, and then do normal operations.

Now we split this up into two equations.

So our solutions are   and 

 

Example Question #2 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve 

Possible Answers:

Correct answer:

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

, , and  correspond to coefficients in the quadratic equation, which is

In this case  ,  , and  .

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an , outside the square root sign, and then do normal operations.

Now we split this up into two equations.

So our solutions are  and 

 

Example Question #3 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve 

Possible Answers:

Correct answer:

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

, , and  correspond to coefficients in the quadratic equation, which is

In this case  ,  , and  .

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an , outside the square root sign, and then do normal operations.

Now we split this up into two equations.

So our solutions are  and 

 

Example Question #4 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve 

Possible Answers:

Correct answer:

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

, , and  correspond to coefficients in the quadratic equation, which is

In this case  ,  , and .

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an , outside the square root sign, and then do normal operations.

Now we split this up into two equations.

So our solutions are   and 

 

Example Question #5 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve 

Possible Answers:

Correct answer:

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

, , and  correspond to coefficients in the quadratic equation, which is

In this case  ,  , and .

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an , outside the square root sign, and then do normal operations.

Now we split this up into two equations.

So our solutions are  and 

 

Example Question #6 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve 

Possible Answers:

Correct answer:

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

, , and  correspond to coefficients in the quadratic equation, which is

In this case  , , and  .

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an , outside the square root sign, and then do normal operations.

Now we split this up into two equations.

So our solutions are  and 

 

Example Question #7 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve 

Possible Answers:

Correct answer:

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

, , and  correspond to coefficients in the quadratic equation, which is

In this case  , , and .

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an \uptext{i}, outside the square root sign, and then do normal operations.

Now we split this up into two equations.

So our solutions are   and 

 

Example Question #8 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve 

Possible Answers:

Correct answer:

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

, , and  correspond to coefficients in the quadratic equation, which is

In this case  ,  , and  .

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an , outside the square root sign, and then do normal operations.

Now we split this up into two equations.

So our solutions are   and 

 

Example Question #9 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve 

Possible Answers:

Correct answer:

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

, , and  correspond to coefficients in the quadratic equation, which is

In this case , , and .

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an , outside the square root sign, and then do normal operations.

Now we split this up into two equations.

So our solutions are   and 

 

Example Question #10 : Solve Quadratic Equations By Inspection, Quadratic Formula, Factoring, Completing The Square, And Taking Square Roots: Ccss.Math.Content.Hsa Rei.B.4b

Solve 

Possible Answers:

Correct answer:

Explanation:

We can solve this by using the quadratic formula.

The quadratic formula is

, , and  correspond to coefficients in the quadratic equation, which is

In this case  ,  , and .

Since the number inside the square root is negative, we will have an imaginary answer.

We will put an , outside the square root sign, and then do normal operations.

Now we split this up into two equations.

So our solutions are   and 

 

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