Free Printable Quadratic Equations Worksheet

The dynamic generator tool below creates a printable math worksheet with 20 quadratic equation questions. The coefficients in each problem are randomly generated, so each time you click the button, you will get a completely different set of exercises. All of the problems are in the moderate to challenging range. Use the worksheets to supplement homeschooling curriculum, for after school tutoring, or to practice ACT and SAT math.

Solution Hints

Problems 2, 3, 4, 5 :
Combine like terms and either factor the expression or use the quadratic formula. The solution set may be one real number, two real numbers, or two complex numbers.

Problems 6, 13, 14 :
The system represents the intersection of a parabola and line. Use substitution to create a quadratic equation in one variable, solve it, then plug your solution(s) into one of the equations to find the value(s) of the other variable. If either x or y is a complex number then the parabola and line have no intersection point(s). The solution set may be one coordinate pair, two coordinate pairs, or no solution.

Problems 7, 8 :
Expand the left side and combine like terms, then either factor or use the quadratic formula. The solution set may be one real number, two real numbers, or two complex numbers.

Problems 10, 19 :
Multiply both sides of the equation by x, then either factor or use the quadratic formula. The solution set may be one real number, two real numbers, or two complex numbers.

Problems 11, 12, 16 :
When the radical is by itself on one side of the equation, square both sides. Then combine like terms and either factor or use the quadratic formula. After you solve for x, plug the value(s) back into the original equation to make sure it is a consistent solution. If x is a complex number or the quantity under the radical is negative, then x is not a solution. The solution set may be one real number, two real numbers, or no solution.

Problems 9, 15, 17, 18 :
Cross multiply, then combine like terms. Either factor the equation or use the quadratic formula to solve for x. Plug your answer(s) back into the original fractions to make sure the denominator is defined (non-zero). The solution set may be one real number, two real numbers, two complex numbers, or no solution.

Problems 20 :
Multiply both sides of the equation by x², then either factor or use the quadratic formula. The solution set may be one real number, two real numbers, or two complex numbers.

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