Quadratic Formula Worksheet Puzzle
Each question corresponds to a matching answer that will reveal one letter from the code. Not only does this make it fun and rewarding for students but it also makes it easy for students and teachers to know if the worksheet has been completed correctly. The code consists of random letters so the students have to solve the problem rather than try to guess a sentence from a riddle.
Download the Solving quadratic equations using the quadratic formula puzzle here.
Although there are several techniques for solving quadratic equations, usually the simplest way to solve ax^2 + bx + c = 0 is to factor the quadratic, set the expression equal to 0, and then find the value of x that would set each factor equal to zero. However, sometimes the quadratic is too hard or does not factorize at all, or you cannot work out what the correct factoring should be. But, the Quadratic Formula can always calculate the solution for you if there is one.
The codebreaker activity featured here asks students to use the quadratic formula to solve a variety of quadratic equations to practice their skills of algebraic manipulation and use of the formula; several equations require rearranging before the formula can be applied.
The Quadratic Formula uses "a", "b", and "c" from "ax^2 + bx + c", where "a", "b", and "c" are just numbers; they are called the "coefficients" of the quadratic equation. The Quadratic Formula can be derived by applying the technique of completing the square to the general form of this expression.
The Quadratic Formula must have the equation you have been asked to solve in the form ax^2 + bx +c = 0 before the quadratic formula can be applied. To solve this codebreaker puzzle students will have to rearrange some of the equations first so that they are in this format.
An example of one of the Quadratic Formula problems the students will have to solve in this activity is:
Solve x(6x + 1) = 11
Students will have to rearrange into the correct format
6x^2 + x – 11 = 0
Applying the quadratic formula with a = 6, b= 1 and c = -11 gives the solutions:
x = 1.27 , x = -1.44 to 2 decimal places.
The answer key is included:
There is an explanation of the history and derivation of the quadratic formula here.
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