The Steps to Solve Quadratic Equations


The quadratic equation is most often used to solve curves on a graph when an object is experiencing projectile motion. The sides of the curve intersect the x-axis twice and y-axis once. The two answers the equation yields are the x-axis intersectioning points. The equation uses coefficients, a number multipied by a variable, and is equal to zero. Once you plug in your known values for the coefficients, you can solve for x.

Set Up the Equation

  • Write the quadratic equation on a piece of paper. If you are solving for "x," the equation should read x = (-b ± √((b^2)-4ac)))/2a. The equation yields two answers for "x," corresponding to their location on the x-axis. The equation reads "x" equals the opposite of "b" plus or minus the square root of "b" squared minus 4 times "a" times "c" divided by 2 times "a." Also write the values you know about your curve; for example, if "a" equals 3, "b" equals 20 and "c" equals 10. Plug your known values into the quadratic equation. Using the example numbers given, you have x = (-5 ± √((20^2)-(4x3x10)))/(2x3).

Solve the Equation

  • Solve the equation according to the order of operations to obtain a value for "x." Solve the value that is squared first and the numbers that are multiplied by each other second. The example now reads x = (-5 ± √(400-120))/6. Solve the subraction before solving for the square root phrases in the equation. The example now reads x = (-5 ± 16.73)/6.

Reaching the Answer

  • Solve for "x" by adding or subtracting the numbers on the top of the equation and dividing it by the number on the bottom. The equation uses a ± sign, read plus or minus sign, because the equation needs to yield two values. The two values represent where the two sides of the curve intersect the x-axis on a graph. The answers to the example problem are x = -3.62 and x = 1.96.

Plot the Points

  • On a graph, the first value is to the left of the y-axis on the negative side of the x-axis; the second value is to the right of the y-axis, on the positive side. Having these values enables you to solve for other properties of the curve, such as area.

Related Searches


  • Photo Credit Jupiterimages/ Images
Promoted By Zergnet



Related Searches

Check It Out

Can You Take Advantage Of Student Loan Forgiveness?

Is DIY in your DNA? Become part of our maker community.
Submit Your Work!