Algebra Essentials Formula Sheet

What you will learn

A formula sheet is most useful when every symbol and condition is understood. Do not select a formula only because the numbers seem to fit. First name the target quantity, list known values with units, and check restrictions such as nonzero denominators. After substitution, verify that the answer has a sensible sign, magnitude, and unit.

Core ideas

• Slope: m=(y2-y1)/(x2-x1), with x2 not equal to x1.
• Slope-intercept form: y=mx+b; point-slope form: y-y1=m(x-x1).
• Quadratic formula: x=(-b±√(b²-4ac))/(2a), where a is not zero.
• Percent change: (new-old)/old × 100 percent, where the original value is not zero.

A practical way to use this resource

1. Identify the relationship and write the formula before substituting.
2. Use parentheses around negative values and calculate the numerator and denominator separately.
3. Retain enough precision during working, then round once at the end if directions require it.
4. Check by substitution, estimation, a graph, or an inverse operation.

Check your understanding

For points (-2,5) and (4,-1), calculate slope and write an equation of the line. Then solve 2x²-3x-2=0 with the quadratic formula and verify both solutions by substitution.

Accuracy and next steps

Use this page as a learning guide, compare your work with course requirements, and ask an instructor when a local rule or assignment direction differs.