Quadratic Formula Game
The quadratic formula to solve any quadratic equation in the form ax² + bx + c = 0, where a, b, and c are coefficients. The formula works even for equations that don’t factor easily or can’t be factored at all using integers. The formula is given as:
\( x = \frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\)
Scroll down the page for a more detailed explanation.
 
Thus game will require you to solve a quadratic equation where the equation cannot be factored easily. Use the formula to find the values for x. Round any decimals to two decimal places. If you get an answer wrong, the game will show you the correct solution.
 
Check out this other two games that solve quadratic equations by factoring:
Solve Quadratic Equations (a = 1)
Solve Quadratic Equations (a > 1)
 

 

How to Play the Quadratic Formula Game
Thus game will challenge you solve a quadratic equation using the quadratic formula.
Here’s how to play:

1. Timed Option: Check the timer if you want to enable the 60 second timer. Click “Start Game”.
   
2. Look at the Problem: You’ll be given a quadratic equation in the form x² + bx + c = 0.
   
3. Enter Your Answer: Enter in the 2 values for x. Round decimals to 2 decimal places.
   
4. Check Your Work: Click the Check button (or press the Enter key). The game will tell you if you’re correct. If you are wrong, you will be shown the correct answer.
   
5. Get a New Problem: Click the Next button for a new problem.
   Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried.
6. Back to Menu Click “Back to Menu” to restart the game.
    
   

How to use the Quadratic Formula
Step 1: Standardize the equation
Rewrite your equation in the standard form: ax² + bx + c = 0.
Step 2: Identify the coefficients
From the standard form, identify the values for a, b, and c. Be sure to include the sign of each coefficient.
Step 3: Substitute values into the quadratic formula
Plug the values of a, b, and c into the formula: \( x = \frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\)
Using parentheses when substituting is a good practice to avoid errors, especially with negative numbers.
Step 4: Simplify the expression
Calculate the value inside the square root first \( (b^{2}-4ac) \). This part is called the discriminant.
Simplify the square root.
Perform the addition and subtraction with the \(\pm \) sign to get two separate solutions: one using the plus sign and one using the minus sign.
Divide the result by \(2a\).
Step 5: Check your solutions
Substitute each of the two (x) values back into the original quadratic equation to verify that they both satisfy the equation.
 

The video gives a clear, step-by-step approach to solving quadratic equations using the quadratic formula.

• Show Video

 

Free Algebra Games

• Algebraic Expressions

  Evaluate Algebraic Expressions
  Evaluate Expressions (Exponents)
  

  Distributive Property
  Distributive Property (Exponents)
  

  Simplify Algebraic Expressions
  Add or Subtract Polynomials
  

  Multiply Binomials (y+b)(y+d)
  Multiply Binomials (ay+b)(cy+d)
  

  Factor Linear Expressions
  Factor Binomials
  Factor Difference of Two Squares
  Factor Perfect Square Trinomials
  Factor Trinomials
  

• Algebraic Equations

  Solve Equations (1-step or 2-step)
  Solve Equations with variables on both sides
  Combine Like Terms & Solve Equations (2(3x-2) + 9 = -5x)
  

  Solve for a Variable (add or subtract)
  Solve Literal Equations (multiply or divide)
  

  Standard Form to Slope-Intercept Form
  Slope-Intercept Form to Standard Form
  

  Solve Quadratic Equations (a = 1)
  Solve Quadratic Equations (a > 1)
  Solve Quadratic Equations (use the quadratic formula)
  

  Solve Systems of Equations (by substitution)
  Solve Systems of Equations (by elimination)
  

• Algebraic Inequalities

  Inequalities on the Number Line (may not work well on the mobile)
  Solve Inequalities (1-step or 2-step)
  

 

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

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