Answer:
Option B) minimum value at −10
Step-by-step explanation:
we have
[tex]f(x)=x^{2} -10x+15[/tex]
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
[tex]f(x)-15=x^{2} -10x[/tex]
Divide the coefficient of term x by 2
10/2=5
squared the term and add to the right side of equation
[tex]f(x)-15=(x^{2} -10x+5^2)[/tex]
Remember to balance the equation by adding the same constants to the other side
[tex]f(x)-15+5^2=(x^{2} -10x+5^2)[/tex]
[tex]f(x)+10=(x^{2} -10x+25)[/tex]
rewrite as perfect squares
[tex]f(x)+10=(x-5)^{2}[/tex]
[tex]f(x)=(x-5)^{2}-10[/tex] ----> function in vertex form
The vertex of the quadratic function is the point (5,-10)
therefore
The minimum value of the function is -10
