Answer:
<em>Her raise per hour is $3.</em>
Step-by-step explanation:
<u>Quadratic Equation</u>
The standard representation of a quadratic equation is:
![ax^2+bx+c=0](https://tex.z-dn.net/?f=ax%5E2%2Bbx%2Bc%3D0)
where a,b, and c are constants.
It can be solved by using the quadratic formula:
![\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-b%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D)
Jill asks for an increase in the hourly wage she receives. Since she works in a Maths Center, the increase comes as a maths equation.
She must solve the equation:
![x^2-6x+9=0](https://tex.z-dn.net/?f=x%5E2-6x%2B9%3D0)
The solution to the equation is the increase in her hourly wage.
Comparing with the general form, we have a=1, b=-6, c=9. Thus, the solutions are:
![\displaystyle x=\frac{-(-6)\pm \sqrt{(-6)^2-4(1)(9)}}{2(1)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B-%28-6%29%5Cpm%20%5Csqrt%7B%28-6%29%5E2-4%281%29%289%29%7D%7D%7B2%281%29%7D)
![\displaystyle x=\frac{6\pm \sqrt{36-36}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B6%5Cpm%20%5Csqrt%7B36-36%7D%7D%7B2%7D)
![\displaystyle x=\frac{6\pm \sqrt{0}}{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B6%5Cpm%20%5Csqrt%7B0%7D%7D%7B2%7D)
Since the square root is 0, there is only one solution:
![\displaystyle x=\frac{6}{2}=3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%3D%5Cfrac%7B6%7D%7B2%7D%3D3)
x = 3
Thus, her raise per hour is $3.