College Algebra Cheat Sheet

Questions and Answers

What are the steps for solving linear equations?

Simplify (distribution, combine like terms). 2. Move x to one side by adding/subtracting. 3. Add/subtract the constant on the variable side to each side. 4. Multiply or divide by coefficient to each side.

What are the characteristics of linear functions?

No exponents on the variable.

What are the steps for solving quadratic equations?

Make equal to zero. 2. Write in order ax^2 + bx + c. 3. Factor, use the quadratic formula.

What are the steps for factoring quadratics?

<ol> <li>Multiply a * c. 2. Make a factor/sum table of a * c. 3. Match the exact sum to b. 4. Rewrite equation as these factors: (x + one factor of the factor sum)(x + other factor of factor sum). 5. If a = 1 you're done; if a is not 1, divide each constant by 'a' and reduce.</li> </ol> Signup and view all the answers

What is the quadratic formula?

<p>x = (-b ± √(b^2 - 4ac)) / 2a</p> Signup and view all the answers

What are the characteristics of quadratics?

<ol> <li>Variable has to have a degree of 2. 2. Has at most 2 answers. 3. Most of the time has three terms.</li> </ol> Signup and view all the answers

What are the steps for solving square roots?

<ol> <li>Solve for the square root by adding/subtracting and/or multiplying/dividing. 2. Square each side. 3. Repeat till no more square roots, then solve for x.</li> </ol> Signup and view all the answers

What are the characteristics of square roots?

<p>Has a square root symbol.</p> Signup and view all the answers

What are the steps for solving absolute values?

<ol> <li>Solve for absolute value. 2. Get rid of absolute value signs and make 2 equations. Make them equal the value of the answer: one positive, one negative.</li> </ol> Signup and view all the answers

Study Notes

Solving Linear Equations

Begin by simplifying the equation using distribution and combining like terms.
Isolate the variable ( x ) on one side through addition or subtraction.
Adjust the constant on the variable side by adding or subtracting it from both sides.
To isolate ( x ), multiply or divide each side by the coefficient of ( x ).

Characteristics of Linear Functions

Linear functions are defined by having no exponents on the variable.

Solving Quadratic Equations

Set the equation equal to zero.
Arrange it in standard form: ( ax^2 + bx + c ).
Solve the equation by factoring or using the quadratic formula.

Factoring Quadratics

Begin by multiplying ( a ) and ( c ) (the leading coefficient and constant).
Create a factor/sum table based on the product ( ac ).
Identify factors that add up to ( b ).
Rewrite the quadratic equation using the identified factors: ( (x + \text{factor1})(x + \text{factor2}) ).
If ( a = 1 ), the process is complete. If not, divide each constant by ( a ) and simplify; the denominators shift to the front of the variable.

Quadratic Formula

The quadratic formula is expressed as ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ) for finding solutions of quadratic equations.

Characteristics of Quadratics

The variable in quadratic equations must have a degree of 2.
Quadratic equations can have a maximum of two solutions.
Typically structured with three terms.

Square Roots

To solve for square roots, apply addition or subtraction and/or multiplication/division.
Square each side of the equation to eliminate the roots.
Continue the process until there are no remaining square roots and isolate ( x ).

Characteristics of Square Roots

Square root equations are typically identified by the presence of a square root symbol.

Solving Absolute Values

Start by addressing the absolute value expression directly.
Remove absolute value signs to create two separate equations—one set equal to the positive value and one to the negative equivalent of the answer.

Description

This quiz covers essential concepts in college algebra, including solving linear and quadratic equations, and understanding the characteristics of linear functions. Perfect for quick revision or study sessions, the flashcards help reinforce key definitions and processes in algebra.