Solve quadratic function word problems by determining each term of the quadratic equation and then solving for x when the equation is equal to zero. A quadratic equation is expressed as ax^2 + bx + c = 0 when in standard form.
- Identify the terms in the quadratic equation
If your word problem does not directly provide the quadratic equation needed to solve the problem, use the information provided to create the equation. An example is a word problem asking when would an object, thrown upward from a specific height and speed, hit the ground. In this problem, a equals the starting height, b equals its upward speed and c equals the change of speed due to gravity.
- Factor the equation in terms of x
To evaluate the word problem, solve the determined quadratic equation in terms of x by factoring into a form (px + q)(rx + s) = 0.
- Solve for x
Set each term of the equation (px + q)(rx + s) = 0 equal to zero to find the two possible values for x in the equation.
- Choose the proper x value
Use the word problem to determine which value for x is correct. For example, if the problem asks for the time at which a thrown object reaches the ground and one value time is positive and one value is negative, choose the positive value as negative time would not make sense in the context of the word problem.