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Using the Quadratic Formula

HSA-REI.B.4b
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High School - HSA-REI.B.4b

How to use the Quadratic Formula? The easiest way to solve the quadratic equation is to factor the quadratic for the value of 'x.' We equate each factor equal to zero and then find the solution for each factor. Where factoring seems challenging, the quadratic formula makes it easier to find the solutions. If you use the general quadratic equation, ax^2 + bx + c = 0 Then you will be able to find the roots of the quadratic equation i.e., values of 'x' for which the equation is being solved THE QUADRATIC FORMULA - Quadratic Formula also uses 'a' , 'b' , and 'c' to represent the numerical coefficients. Quadratic Formula is written as: X = (-b±√(b^2 )-4ac)/2a Let's understand this better with an example WORKED EXAMPLE - First, identify the values for a, b, and c. make sure you write your equation in the format of quadratic equation, i.e., ax2+bx+c=0 Let's assume if we have, x2 + 4x – 21 = 0 | a is the coefficient with x2, so in this case, we have a=1, b is the coefficient with x, here b=4, c is the numerical constant, so here c = -21 replace all the values in the formula: x = (-4 ±√16-4.1.(-21))/(2.1) solving the equation for the value of x x = (-4 ± √100)/2 | x = (-4 ±10)/2 | x = (-4+10)/2,(-4-10)/2 | x = 6/(2 ) ,(-14)/2 | x = 3, -7 | the values of 'x' are 3, and -7

Printable Worksheets And Lessons






Homework Sheets

This is an important section for students. They can use all the practice that they can get.

  • Homework 1 - Where a ≠ 0. We can use it to solve a quadratic equation (ax^2 + bx + c = 0).
  • Homework 2 - Now we will use the quadratic formula to solve 5y^2 + 5y – 5 = 0.
  • Homework 3 - In this case a = 1 b = -4 c = 2. We plug those values in the formula we have been using.



Practice Worksheets

This skill is found in so many different forms of science that it is key to motion in many respects.

  • Practice 1 - Solve the equations using the quadratic formula.
  • Practice 2 - Just plug and chug away at this formula.
  • Practice 3 - Solve for each variable using the quadratic formula.



Math Skill Quizzes

My husband was a salesman for years and always used the quadratic formula to forecast sales.

  • Quiz 1 - This technique is used often to gauge the speed of UFOs.
  • Quiz 2 - Most economists used this formula to predict profits.
  • Quiz 3 - When the equipment is down in a submarine, the quadratic formula is used to determine the impacts of torpedoes.