Complete the square to determine the minimum or maximum value of the function defined by the expression.x2 − 10x + 15A) maximum value at −10 B) minimum value at −10 C) maximum value at −15 D) minimum value at −15

Answer:Option B) minimum value at −10Step-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 minimumGroup 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 210/2=5squared 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 formThe vertex of the quadratic function is the point (5,-10)thereforeThe minimum value of the function is -10