INTRODUCTION
A quadratic equation is an equation of the form \( ax^2+bx+c=0 \) where \(a\), \(b\) and \(c\) are constants, \( a \neq 0 \).
A quadratic function is a function of the form \( y=ax^2+bx+c\), \( a \neq 0\).
The profit function of a computer manufacturing company is given by \[ P(x)=-x^2+25x-24\] where \(x\) is the number of units produced (in thousands) and the profit \(P(x)\) is in thousand dollars. Determine how many units should be produced for a profit of at least \(40\) thousand dollars.
Clearly, we need to solve the following equation: \[-x^2+25x-24=40\]
We can rearrange the equation to give \[ x^2-25x+64=0\]
The equation \(x^2-25x+64=0\) is of the form \( ax^2+bx+c=0 \) and is, therefore, a quadratic equation.
A quadratic function is a function of the form \( y=ax^2+bx+c\), \( a \neq 0\).
The profit function of a computer manufacturing company is given by \[ P(x)=-x^2+25x-24\] where \(x\) is the number of units produced (in thousands) and the profit \(P(x)\) is in thousand dollars. Determine how many units should be produced for a profit of at least \(40\) thousand dollars.
Clearly, we need to solve the following equation: \[-x^2+25x-24=40\]
We can rearrange the equation to give \[ x^2-25x+64=0\]
The equation \(x^2-25x+64=0\) is of the form \( ax^2+bx+c=0 \) and is, therefore, a quadratic equation.
SOLVING A QUADRATIC EQUATION
We may use following methods to solve a quadratic equation.
- factoring quadratic equation and using NULL FACTOR law
- completing the square method
- using technology (graphing calculator, geogebra)
- using the quadratic formula