Exponential Functions
Linera Equations
Simple Trinomials as Products of Binomials
Laws of Exponents and Dividing Monomials
Solving Equations
Multiplying Polynomials
Multiplying and Dividing Rational Expressions
Solving Systems of Linear Inequalities
Mixed-Number Notation
Linear Equations and Inequalities in One Variable
The Quadratic Formula
Fractions and Decimals
Graphing Logarithmic Functions
Multiplication by 111
Solving Systems of Equations - Two Lines
Solving Nonlinear Equations by Factoring
Solving Linear Systems of Equations by Elimination
Rationalizing the Denominator
Simplifying Complex Fractions
Factoring Trinomials
Linear Relations and Functions
Axis of Symmetry and Vertices
Equations Quadratic in Form
The Appearance of a Polynomial Equation
Subtracting Reverses
Non-Linear Equations
Exponents and Order of Operations
Factoring Trinomials by Grouping
Factoring Trinomials of the Type ax 2 + bx + c
The Distance Formula
Invariants Under Rotation
Multiplying and Dividing Monomials
Solving a System of Three Linear Equations by Elimination
Multiplication by 25
Powers of i
Solving Quadratic and Polynomial Equations
Slope-intercept Form for the Equation of a Line
Equations of Lines
Square Roots
Integral Exponents
Product Rule for Radicals
Solving Compound Linear Inequalities
Axis of Symmetry and Vertices
Multiplying Rational Expressions
Reducing Rational Expressions
Properties of Negative Exponents
Numbers, Factors, and Reducing Fractions to Lowest Terms
Solving Quadratic Equations
Factoring Completely General Quadratic Trinomials
Solving a Formula for a Given Variable
Factoring Polynomials
Decimal Numbers and Fractions
Multiplication Properties of Exponents
Multiplying Fractions
Multiplication by 50

Try the Free Math Solver or Scroll down to Tutorials!












Please use this form if you would like
to have this math solver on your website,
free of charge.


To factor a quadratic expression means to write it as the product of two linear expressions.

To factor x2 + bx + c, find the numbers p and q such that p + q = b and pq = c.


x2 +7x + 10 = (x + 5)(x + 2)

5 + 2 = 7 and 5 × 2 = 10

To factor ax2 + bx + c where a ≠ 1, find the factors of a (m and n) and c ( p and q) so that the sum of the outer and inner products (mq and pn) is b.

ax2 + bx + c = (mx + p)(nx + q)



x2 + 4x - 12 matches (x + 6)(x - 2)

“The factor pairs for 12 are 12 and 1, 6 and 2, and 3 and 4. Because the last term in the quadratic expression is negative, one factor is positive and one is negative. These factors must have a sum of 4, so the factored expression is (x + 6)(x - 2).”



A quadratic function has a U-shaped graph called a parabola. A quadratic function can be written in the form ax2 + c, where a is called the leading coefficient. If a is positive, the parabola opens up. If a is negative, the parabola opens down. If the absolute value of a is greater than 1, then the parabola will be narrower than y = x2. If the absolute value of a is less than 1, then the parabola will be wider than y = x2.

The vertex of a parabola is the point from which the graph opens up or down.

Adding values to and subtracting values from ax2 translates the vertex along the y-axis.

In the form y = (x - a)(x - b), the vertex is located at (a, b) .


matches .

“The vertex is at (0, 4). Because the leading coefficient is positive, the graph opens up. Because the leading coefficient is less than 1, the graph will be wider than y = x2