High School Math : Solving Quadratic Equations

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : Completing The Square

Find the vertex of the parabola by completing the square.

Possible Answers:

Correct answer:

Explanation:

To find the vertex of a parabola, we must put the equation into the vertex form:

The vertex can then be found with the coordinates (h, k).

To put the parabola's equation into vertex form, you have to complete the square. Completing the square just means adding the same number to both sides of the equation -- which, remember, doesn't change the value of the equation -- in order to create a perfect square.

Start with the original equation:

Put all of the  terms on one side:

Now we know that we have to add something to both sides in order to create a perfect square:

In this case, we need to add 4 on both sides so that the right-hand side of the equation factors neatly.

Now we factor:

Once we isolate , we have the equation in vertex form:

Thus, the parabola's vertex can be found at .

Example Question #31 : Solving Quadratic Equations

Complete the square:

Possible Answers:

Correct answer:

Explanation:

Begin by dividing the equation by  and subtracting  from each side:

Square the value in front of the  and add to each side:

Factor the left side of the equation:

Take the square root of both sides and simplify:

Example Question #54 : Quadratic Equations And Inequalities

Use factoring to solve the quadratic equation:

Possible Answers:

Correct answer:

Explanation:

Factor and solve:

Factor like terms:

Combine like terms:

Example Question #1 : Completing The Square

Complete the square:

Possible Answers:

Correct answer:

Explanation:

Begin by dividing the equation by  and adding  to each side:

Square the value in front of the  and add to each side:

Factor the left side of the equation:

Take the square root of both sides and simplify:

Example Question #331 : Algebra Ii

Complete the square:

Possible Answers:

Correct answer:

Explanation:

Begin by dividing the equation by  and subtracting  from each side:

Square the value in front of the  and add to each side:

Factor the left side of the equation:

Take the square root of both sides and simplify:

Example Question #1 : Using The Quadratic Formula

Solve using the quadratic formula:

Possible Answers:

Correct answer:

Explanation:

Use the quadratic formula to solve:

Example Question #1 : Using The Quadratic Formula

Solve using the quadratic formula:

Possible Answers:

Correct answer:

Explanation:

Use the quadratic formula to solve:

Example Question #1 : Using The Quadratic Formula

Solve using the quadratic formula:

Possible Answers:

Correct answer:

Explanation:

Use the quadratic formula to solve:

Example Question #4 : Using The Quadratic Formula

Solve using the quadratric formula:

Possible Answers:

Correct answer:

Explanation:

Use the quadratic formula to solve:

Example Question #1631 : High School Math

A baseball that is thrown in the air follows a trajectory of , where  is the height of the ball in feet and  is the time elapsed in seconds. How long does the ball stay in the air before it hits the ground?

Possible Answers:

Between 2 and 2.5 seconds

Between 2.5 and 3 seconds

Between 3.5 and 4 seconds

Between 3 and 3.5 seconds

 Between 4 and 4.5 seconds 

Correct answer:

Between 3 and 3.5 seconds

Explanation:

To solve this, we look at the equation .

Setting the equation equal to 0 we get .

Once in this form, we can use the Quadratic Formula to solve for .

The quadratic formula says that if , then 

.

Plugging in our values:

 

Therefore or  and since we are looking only for positive values (because we can't have negative time), 3.4375 seconds is our answer.

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