Solving Practical Problems Involving Quadratic Equations

Projectile Motion

Illustration showing the trajectory of a punted football.

As discussed in the Module Overview, quadratic equations can be used to model the motion of a projectile and determine the height of the object at specified times. The height, h, in feet, of an object t seconds after it has been launched can be modeled by the formula, h = −16t2 + v0t + h0 where v0 represents the initial velocity of the object, in feet per second, and h0 represents the initial height of the object, in feet. In this topic, you will learn how to use this formula to model and solve problems involving projectile motion.

Practical Problems Involving Quadratic Equations

Practical Problems Involving Quadratic Equations interactivityPrepare to apply your knowledge of quadratic equations as you work to solve real-world problems. In this interactivity, you will use quadratic equations to model and solve practical problems involving area and projectile motion. Click the player to begin.

View a printable version of this interactivity.

 

 

Finding the Solutions to the Quadratic Equation by Graphing

Quadratic equations can be represented graphically. Take a look at the following example

Example:

A practical problem and graphical representation

The area of the given rectangle is modeled by a quadratic equation, whose graph is shown above. You can determine the solutions to the quadratic equation by identifying the x-intercepts. In this example, the solutions are x = −6 or x = 1. You can determine which of the solutions is extraneous by substituting the values in the expressions that model the length and width of the rectangle. You will continue to explore graphical representations of quadratic equations when you begin your study of function families in a future module.

 

Solving Practical Problems Involving Quadratic Equations Review

self-check iconSolving Real-World Problems Involving Quadratic Equations ReviewNow that you have explored how to solve practical problems involving quadratic equations, review your knowledge in this interactivity. Click the player button to get started.

 

 

 

digital repository iconDid you answer the content questions incorrectly? Do you need more instruction or extra practice? If so, view the video Solving Quadratic Equations Graphically from eMediaVASM.