Answer:
Option B) minimum value at −10
Step-by-step explanation:
we have
![f(x)=x^{2} -10x+15](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E%7B2%7D%20-10x%2B15)
This function represent a vertical parabola open upward (because the leading coefficient is positive)
The vertex represent a minimum
Group terms that contain the same variable, and move the constant to the opposite side of the equation
![f(x)-15=x^{2} -10x](https://tex.z-dn.net/?f=f%28x%29-15%3Dx%5E%7B2%7D%20-10x)
Divide the coefficient of term x by 2
10/2=5
squared the term and add to the right side of equation
![f(x)-15=(x^{2} -10x+5^2)](https://tex.z-dn.net/?f=f%28x%29-15%3D%28x%5E%7B2%7D%20-10x%2B5%5E2%29)
Remember to balance the equation by adding the same constants to the other side
![f(x)-15+5^2=(x^{2} -10x+5^2)](https://tex.z-dn.net/?f=f%28x%29-15%2B5%5E2%3D%28x%5E%7B2%7D%20-10x%2B5%5E2%29)
![f(x)+10=(x^{2} -10x+25)](https://tex.z-dn.net/?f=f%28x%29%2B10%3D%28x%5E%7B2%7D%20-10x%2B25%29)
rewrite as perfect squares
![f(x)+10=(x-5)^{2}](https://tex.z-dn.net/?f=f%28x%29%2B10%3D%28x-5%29%5E%7B2%7D)
----> function in vertex form
The vertex of the quadratic function is the point (5,-10)
therefore
The minimum value of the function is -10