Quadratic functions are used widely in science, business and engineering to model physical phenomena and how quantities change over time. The physical parabolic shape of a quadratic can describe the movement of water in a fountain, the movement of a ball (and in fact any object thrown into the air), or the shape of satellite dishes.
When solving practical problems these steps might be helpful:
When at the solution stage of the problem useful starting points are:
Then we employ one of our solving methods:
Solve the following equation:
Write all solutions on the same line, separated by commas.
The area of a rectangle is $160$160 square metres. If the length of the rectangle is $6$6 m longer than its width, find the dimensions.
Let $w$w be the width of the rectangle in metres.
First find the width of the rectangle by solving for $w$w.
Now find the rectangle's length.
The product of 2 consecutive, positive odd numbers is $399$399. Let the smaller number be $2x+1$2x+1.
First solve for $x$x.
Now find the first odd number.
Lastly, find the other odd number.
Solve the following equation for $x$x by substituting in $m=4^x$m=4x.
Use a comma to separate multiple solutions.
Solve quadratic equations for real roots.
Find the solution set for quadratic inequalities.
Use substitution to form and solve a quadratic equation in order to solve a related equation.