High School Math : Intermediate Single-Variable Algebra

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #34 : Solving Quadratic Equations

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 #35 : 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 #1 : Using The Quadratic Formula

Solve using the quadratic formula:

Possible Answers:

Correct answer:

Explanation:

Use the quadratic formula to solve:

Example Question #2 : Using The Quadratic Formula

Solve using the quadratic formula:

Possible Answers:

Correct answer:

Explanation:

Use the quadratic formula to solve:

Example Question #3 : 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 #5 : Using The Quadratic Formula

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 3 and 3.5 seconds

Between 3.5 and 4 seconds

Between 2 and 2.5 seconds

 Between 4 and 4.5 seconds 

Between 2.5 and 3 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.

Example Question #41 : Solving Quadratic Equations

Solve the quadratric inequality:

Possible Answers:

Correct answer:

Explanation:

Factor and solve.

Since the equation is less than or equal to, you know the inequality will be OR, not AND.

 or 

Example Question #42 : Solving Quadratic Equations

Solve the following quadratic inequality:

Possible Answers:

Correct answer:

Explanation:

Factor and solve. Since the sign is less than or equal to, we know the inequality will be OR, not AND.

 or 

Example Question #43 : Solving Quadratic Equations

Solve the following quadratic inequality:

Possible Answers:

Correct answer:

Explanation:

Use the quadratic formula to solve.

Since the inequality is greater than or equal to, we know the inequality will be AND, not OR.

 

 

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